We introduce elementary and Ф-free Lie triple systems and study the properties of these systems. In particular, structures of subsystems of an elementary Lie triple system and a class of Ф-free Lie triple systems ar...We introduce elementary and Ф-free Lie triple systems and study the properties of these systems. In particular, structures of subsystems of an elementary Lie triple system and a class of Ф-free Lie triple systems are investigated.展开更多
This paper determined the existence of λ-fold pure Mendelsohn triple system of order v satisfying λv(v-1)≡0 (mod 3) and v≥4λ+5, or v=2λ+2, and in the case of λ=4,5,6,which completely settled their existence.
In this paper, we consider Lie triple systems with derivations. A pair consisting of a Lie triple system and a distinguished derivation is called a LietsDer pair. We define a cohomology theory for LietsDer pair with c...In this paper, we consider Lie triple systems with derivations. A pair consisting of a Lie triple system and a distinguished derivation is called a LietsDer pair. We define a cohomology theory for LietsDer pair with coefficients in a representation. We study central extensions of a LietsDer pair. In the next, we generalize the formal deformation theory to LietsDer pairs in which we deform both the Lie triple system bracket and the distinguished derivation. It is governed by the cohomology of LietsDer pair with coefficients in itself.展开更多
An LRHTS（v） （or LARHTS（v）） is a collection of {（X, Bi） ： 1≤i ≤ 4（v - 2）}, where X is a v-set, each （X, Bi） is a resolvable （or almost resolvable） HTS（v）, and all Bis form a partition of all cycle tr...An LRHTS（v） （or LARHTS（v）） is a collection of {（X, Bi） ： 1≤i ≤ 4（v - 2）}, where X is a v-set, each （X, Bi） is a resolvable （or almost resolvable） HTS（v）, and all Bis form a partition of all cycle triples and transitive triples on X. An OLRHTS（v） （or OLARHTS（v）） is a collection {（Y／{y}, Ay^j） ： y ∈ Y,j = 0, 1, 2, 3}, where Y is a （v ＋ 1）-set, each （Y／{y}, Ay^j） is a resolvable （or almost resolvable） HTS（v）, and all Ay^js form a partition of all cycle and transitive triples on Y. In this paper, we establish some directed and recursive constructions for LRHTS（v）, LARHTS（v）, OLRHTS（v）, OLARHTS（v） and give some new results.展开更多
In this paper,we consider compatible Hom-Lie triple systems.More precisely,compatible Hom-Lie triple systems are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra.We also define a...In this paper,we consider compatible Hom-Lie triple systems.More precisely,compatible Hom-Lie triple systems are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra.We also define a cohomology theory for compatible Hom-Lie triple systems.As applications of cohomology,we study linear deformations and abelian extensions of compatible Hom-Lie triple systems.展开更多
For a Lie triple system T over a field of characteristic zero, some sufficient conditions for T to be two-generated are proved. We also discuss to what extent the two-generated subsystems determine the structure of th...For a Lie triple system T over a field of characteristic zero, some sufficient conditions for T to be two-generated are proved. We also discuss to what extent the two-generated subsystems determine the structure of the system T . One of the main results is that T is solvable if and only if every two elements generates a solvable subsystem. In fact, we give an explicit two-generated law for the two-generated subsystems.展开更多
The aim of this article is to study the structures of arbitrary split δ-Jordan Lie triple systems, which are a generalization of split Lie triple systems. By developing techniques of connections of roots for this kin...The aim of this article is to study the structures of arbitrary split δ-Jordan Lie triple systems, which are a generalization of split Lie triple systems. By developing techniques of connections of roots for this kind of triple systems, we show that any of such δ-Jordan Lie triple systems T with a symmetric root system is of the form T=U+∑[α]∈■1/~I[α] with U a subspace of T0 and any I[α] a well described ideal of T, satisfying{I[α],T,I[β]}={I[α],I[β],T}={T,I[α],I[β]}=0 if [α]≠[β] .展开更多
The observations of fully-charm tetraquark states in the LHCb,CMS,and ATLAS experiments suggested the existence of hadronic molecules of two-charmonium states,which may also imply bound states in the threecharmonium s...The observations of fully-charm tetraquark states in the LHCb,CMS,and ATLAS experiments suggested the existence of hadronic molecules of two-charmonium states,which may also imply bound states in the threecharmonium systems.In this work,we study the possible bound states in the triple-ηcand triple-J/ψsystems with J^(PC)=0^(-+)and 1^(--),respectively.In quantum chromodynamics sum rules,we calculate the two-point correlation functions and spectral functions up to the dimension-four gluon condensate.We use the iterative dispersion relation approach to deal with the five-loop banana integrals,which significantly improves computational efficiency.Our results show that the masses of triple-ηcand triple-J/ψstates lie below the corresponding mass thresholds,supporting the existence of such three-body bound states.展开更多
We study the structure of arbitrary split Leibniz triple systems with a coherent O-root space. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of...We study the structure of arbitrary split Leibniz triple systems with a coherent O-root space. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of T being of maximal length＇, the simplicity of the Leibniz triple systems is characterized.展开更多
A bilinear form f on a nonassociative triple system T is said to be invariant if and only if f( abc ,d) = f(a, dcb ) = f(c, bad ) for all a,b,c,d ∈ T . (T ,f) is called a pseudo-metric triple system if f is non-degen...A bilinear form f on a nonassociative triple system T is said to be invariant if and only if f( abc ,d) = f(a, dcb ) = f(c, bad ) for all a,b,c,d ∈ T . (T ,f) is called a pseudo-metric triple system if f is non-degenerate and invariant. A decomposition theory for triple systems and pseudo-metric triple systems is established. Moreover, the ?nite-dimensional metric Lie triple systems are characterized in terms of the structure of the non-degenerate, invariant and symmetric bilinear forms on them.展开更多
Generalized Steiner triple systems, GS(2, 3, n, g) are equivalent to (g+1)-ary maximum constant weight codes (n, 3,3)s. In this paper, it is proved that the necessary conditions for the existence of a GS(2,3, n, 10), ...Generalized Steiner triple systems, GS(2, 3, n, g) are equivalent to (g+1)-ary maximum constant weight codes (n, 3,3)s. In this paper, it is proved that the necessary conditions for the existence of a GS(2,3, n, 10), namely, n ≡ 0,1 (mod 3) and n ≥ 12, are also sufficient.展开更多
As a natural generalization of a restricted Lie algebra, a restricted Lie triple system was defined by Hodge. In this paper, we develop initially the Frattini theory for restricted Lie triple systems, generalize some ...As a natural generalization of a restricted Lie algebra, a restricted Lie triple system was defined by Hodge. In this paper, we develop initially the Frattini theory for restricted Lie triple systems, generalize some results of Frattini p-subalgebra for restricted Lie algebras, obtain some properties of the Frattini p-subsystem and give the relationship between Фp（T） and Ф（T） for solvable Lie triple systems.展开更多
As an important index to measure the degree of entanglement in quantum systems,concurrence plays an important role in practical research.In this paper,we study the concurrence between two qubits in triangular triple q...As an important index to measure the degree of entanglement in quantum systems,concurrence plays an important role in practical research.In this paper,we study the concurrence between two qubits in triangular triple quantum dot structure.Through calculation and simulation,it is found that concurrence is mainly affected by the interdot coupling strength t,Coulomb interactionU,temperature T,and electrode coupling G.Through comparative studies with parallel triple quantum dot structures,we demonstrate that the triangular geometry exhibits significantly enhanced concurrence under identical conditions.In addition,under the condition that concurrence exceeds 0.9,the functional relationship between t and U is obtained through simulation,which provides theoretical support for quantum dot regulation under high entanglement.Finally,we demonstrate the feasibility of implementing a three-qubit quantum gate,using the Toffoli gate as a representative example,under the condition that the triangular triple quantum dot system maintains high entanglement.展开更多
An LPDTS(υ)is a collection of 3(υ-2)disjoint pure directed triple systems on the same set ofυelements.It is showed in Tian's doctoral thesis that there exists an LPDTS(υ)forυ≡0,4(mod 6),υ≥4.In this paper,w...An LPDTS(υ)is a collection of 3(υ-2)disjoint pure directed triple systems on the same set ofυelements.It is showed in Tian's doctoral thesis that there exists an LPDTS(υ)forυ≡0,4(mod 6),υ≥4.In this paper,we establish the existence of an LPDTS(υ)forυ≡1,3(mod 6),υ>3.Thus the spectrum for LPDTS(υ)is completely determined to be the set{υ:υ≡0,1(mod 3),υ≥4}.展开更多
A directed triple system of order v,denoted by DTS(v,λ),is a pair(X,B)where X is a v-set and B is a collection of transitive triples on X such that every ordered pair of X belongs toλtriples of B.An overlarge set of...A directed triple system of order v,denoted by DTS(v,λ),is a pair(X,B)where X is a v-set and B is a collection of transitive triples on X such that every ordered pair of X belongs toλtriples of B.An overlarge set of disjoint DTS(v,λ),denoted by OLDTS(v,λ),is a collection{(Y\{y},Ai)}i,such that Y is a(v+1)-set,each(Y\{y},Ai)is a DTS(v,λ)and all Ai's form a partition of all transitive triples of Y.In this paper,we shall discuss the existence problem of OLDTS(v,λ)and give the following conclusion:there exists an OLDTS(v,λ)if and only if eitherλ=1 and v=0,1(mod 3),orλ=3 and v≠2.展开更多
In this paper, we first define a doubly transitive resolvable idempotent quasigroup （DTRIQ）, and show that aDTRIQ of order v exists if and only ifv ≡0（mod3） and v ≠ 2（mod4）. Then we use DTRIQ to present a trip...In this paper, we first define a doubly transitive resolvable idempotent quasigroup （DTRIQ）, and show that aDTRIQ of order v exists if and only ifv ≡0（mod3） and v ≠ 2（mod4）. Then we use DTRIQ to present a tripling construction for large sets of resolvable directed triple systems, which improves an earlier version of tripling construction by Kang （J. Combin. Designs, 4 （1996）, 301-321）. As an application, we obtain an LRDTS（4·3^n） for any integer n ≥ 1, which provides an infinite family of even orders.展开更多
A hybrid triple system of order v and index A, denoted by HTS（v, λ）, is a pair （X,B） where X is a v-set and B is a collection of cyclic triples and transitive triples on X, such that every ordered pair of X belon...A hybrid triple system of order v and index A, denoted by HTS（v, λ）, is a pair （X,B） where X is a v-set and B is a collection of cyclic triples and transitive triples on X, such that every ordered pair of X belongs to A triples of B. An overlarge set of disjoint HTS（v, λ）, denoted by OLHTS（v, λ）, is a collection {（Y／{y}, .Ai）}i, such that Y is a （v ＋ 1）-set, each （Y／{y}, Ai） is an HTS（v, λ,） and all Ais form a partition of all cyclic triples and transitive triples on Y. In this paper, we shall discuss the existence problem of OLHTS（v, A） and give the following conclusion： there exists an OLHTS（v, λ） if and only if λ= 1, 2, 4, v = 0, 1 （rood 3） and v ≥ 4.展开更多
A Mendelsohn triple system of order v （MTS（v）） is a pair （X,B） where X is a v-set and 5g is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of B. An MTS（v） ...A Mendelsohn triple system of order v （MTS（v）） is a pair （X,B） where X is a v-set and 5g is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of B. An MTS（v） （X,B） is called pure and denoted by PMTS（v） if （x, y, z） ∈ B implies （z, y, x） ∈B. A large set of MTS（v）s （LMTS（v）） is a collection of v - 2 pairwise disjoint MTS（v）s on a v-set. A self-converse large set of PMTS（v）s, denoted by LPMTS＊ （v）, is an LMTS（v） containing [ v-2/2] converse pairs of PMTS（v）s. In this paper, some results about the existence and non-existence for LPMTS＊ （v） are obtained.展开更多
A family(X,B1),(X,B2),...,(X,Bq)of q STS(v)s is aλ-fold large set of STS(v)and denoted by LSTSλ(v)if every 3-subset of X is contained in exactlyλSTS(v)s of the collection.It is indecomposable and denoted by IDLSTS...A family(X,B1),(X,B2),...,(X,Bq)of q STS(v)s is aλ-fold large set of STS(v)and denoted by LSTSλ(v)if every 3-subset of X is contained in exactlyλSTS(v)s of the collection.It is indecomposable and denoted by IDLSTSλ(v)if there exists no LSTSλ(v)contained in the collection for anyλ【λ.In 1995,Griggs and Rosa posed a problem:For which values ofλ】1 and orders v≡1,3(mod 6)do there exist IDLSTSλ(v)?In this paper,we use partitionable candelabra systems(PCSs)and holeyλ-fold large set of STS(v)(HLSTSλ(v))as auxiliary designs to establish a recursive construction for IDLSTSλ(v)and show that there exists an IDLSTSλ(v)forλ=2,3,4 and v≡1,3(mod 6).展开更多
In this paper, we introduce a new concept -- overlarge sets of generalized Kirkman systems （OLGKS）, research the relation between it and OLKTS, and obtain some new results for OLKTS. The main conclusion is： If ther...In this paper, we introduce a new concept -- overlarge sets of generalized Kirkman systems （OLGKS）, research the relation between it and OLKTS, and obtain some new results for OLKTS. The main conclusion is： If there exist both an OLKF（6^k） and a 3-OLGKS（6^k-1,4） for all k ∈{6,7,...,40}／{8,17,21,22,25,26}, then there exists an OLKTS（v） for any v ≡ 3 （mod 6）, v ≠ 21. As well, we obtain the following result： There exists an OLKTS（6u ＋ 3） for u = 2^2n-1 - 1, 7^n, 31^n, 127^n, 4^r25^s, where n ≥ 1,r＋s≥ 1.展开更多
基金supported in part by the National Natural Science Foundation of China(10871192)NSF(A2010000194) of Hebei Province,China
文摘We introduce elementary and Ф-free Lie triple systems and study the properties of these systems. In particular, structures of subsystems of an elementary Lie triple system and a class of Ф-free Lie triple systems are investigated.
文摘This paper determined the existence of λ-fold pure Mendelsohn triple system of order v satisfying λv(v-1)≡0 (mod 3) and v≥4λ+5, or v=2λ+2, and in the case of λ=4,5,6,which completely settled their existence.
基金Supported by the National Natural Science Foundation of China (Grant No. 12161013)the General Project of Guizhou University of Finance and Economics (Grant No. 2021KYYB16)。
文摘In this paper, we consider Lie triple systems with derivations. A pair consisting of a Lie triple system and a distinguished derivation is called a LietsDer pair. We define a cohomology theory for LietsDer pair with coefficients in a representation. We study central extensions of a LietsDer pair. In the next, we generalize the formal deformation theory to LietsDer pairs in which we deform both the Lie triple system bracket and the distinguished derivation. It is governed by the cohomology of LietsDer pair with coefficients in itself.
基金Supported by the National Natural Science Foundation of China(Grant No.11471096)
文摘An LRHTS（v） （or LARHTS（v）） is a collection of {（X, Bi） ： 1≤i ≤ 4（v - 2）}, where X is a v-set, each （X, Bi） is a resolvable （or almost resolvable） HTS（v）, and all Bis form a partition of all cycle triples and transitive triples on X. An OLRHTS（v） （or OLARHTS（v）） is a collection {（Y／{y}, Ay^j） ： y ∈ Y,j = 0, 1, 2, 3}, where Y is a （v ＋ 1）-set, each （Y／{y}, Ay^j） is a resolvable （or almost resolvable） HTS（v）, and all Ay^js form a partition of all cycle and transitive triples on Y. In this paper, we establish some directed and recursive constructions for LRHTS（v）, LARHTS（v）, OLRHTS（v）, OLARHTS（v） and give some new results.
基金Supported by the Scientifc Research Foundation for Advanced Talents of GUFE(Grant No.2022YJ007)the Innovation Exploration and Academic Talent Project of GUFE(Grant No.2022XSXMB11)+4 种基金the Science and Technology Program of Guizhou Province(Grant Nos.QKHZC[2023]372QKHJC-[2024]QN081)the Research Foundation for Science&Technology Innovation Team of Guizhou Province(Grant Nos.QJJ[2023]063QJJ[2024]190)the Doctoral Research Start-Up Fundation of Guiyang University(Grant No.GYU-KY-2024)。
文摘In this paper,we consider compatible Hom-Lie triple systems.More precisely,compatible Hom-Lie triple systems are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra.We also define a cohomology theory for compatible Hom-Lie triple systems.As applications of cohomology,we study linear deformations and abelian extensions of compatible Hom-Lie triple systems.
文摘For a Lie triple system T over a field of characteristic zero, some sufficient conditions for T to be two-generated are proved. We also discuss to what extent the two-generated subsystems determine the structure of the system T . One of the main results is that T is solvable if and only if every two elements generates a solvable subsystem. In fact, we give an explicit two-generated law for the two-generated subsystems.
基金Supported by the National Natural Science Foundation of China(Grant No.11801121)the Natural Science Foundation of Heilongjiang Province(Grant No.QC2018006)the Fundamental Research Fundation for Universities of Heilongjiang Province(Grant No.LGYC2018JC002).
文摘The aim of this article is to study the structures of arbitrary split δ-Jordan Lie triple systems, which are a generalization of split Lie triple systems. By developing techniques of connections of roots for this kind of triple systems, we show that any of such δ-Jordan Lie triple systems T with a symmetric root system is of the form T=U+∑[α]∈■1/~I[α] with U a subspace of T0 and any I[α] a well described ideal of T, satisfying{I[α],T,I[β]}={I[α],I[β],T}={T,I[α],I[β]}=0 if [α]≠[β] .
基金supported by the National Natural Science Foundation of China(Grant No.12175318)the Natural Science Foundation of Guangdong Province of China(Grant No.2023A1515011704)。
文摘The observations of fully-charm tetraquark states in the LHCb,CMS,and ATLAS experiments suggested the existence of hadronic molecules of two-charmonium states,which may also imply bound states in the threecharmonium systems.In this work,we study the possible bound states in the triple-ηcand triple-J/ψsystems with J^(PC)=0^(-+)and 1^(--),respectively.In quantum chromodynamics sum rules,we calculate the two-point correlation functions and spectral functions up to the dimension-four gluon condensate.We use the iterative dispersion relation approach to deal with the five-loop banana integrals,which significantly improves computational efficiency.Our results show that the masses of triple-ηcand triple-J/ψstates lie below the corresponding mass thresholds,supporting the existence of such three-body bound states.
基金Supported by Scientific Research Fund of Heilongjiang Provincial Education Department(Grant No.12541184)
文摘We study the structure of arbitrary split Leibniz triple systems with a coherent O-root space. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of T being of maximal length＇, the simplicity of the Leibniz triple systems is characterized.
文摘A bilinear form f on a nonassociative triple system T is said to be invariant if and only if f( abc ,d) = f(a, dcb ) = f(c, bad ) for all a,b,c,d ∈ T . (T ,f) is called a pseudo-metric triple system if f is non-degenerate and invariant. A decomposition theory for triple systems and pseudo-metric triple systems is established. Moreover, the ?nite-dimensional metric Lie triple systems are characterized in terms of the structure of the non-degenerate, invariant and symmetric bilinear forms on them.
基金Supported by YNSFC(10001026)for the first authorby Tianyuan Mathematics Foundation of NNSFCGuangxi Science Foundation and Guangxi Education Committee for the second author.
文摘Generalized Steiner triple systems, GS(2, 3, n, g) are equivalent to (g+1)-ary maximum constant weight codes (n, 3,3)s. In this paper, it is proved that the necessary conditions for the existence of a GS(2,3, n, 10), namely, n ≡ 0,1 (mod 3) and n ≥ 12, are also sufficient.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10701019 and 10871057)the Fundamental Research Funds for the Central Universities, the ZJZSF (Grant Nos. Y607136, D7080080)+1 种基金Qianjiang Excellence Project (Grant No. 2007R10031)the New Century 151 Talent Project (2008) of Zhejiang Province
文摘As a natural generalization of a restricted Lie algebra, a restricted Lie triple system was defined by Hodge. In this paper, we develop initially the Frattini theory for restricted Lie triple systems, generalize some results of Frattini p-subalgebra for restricted Lie algebras, obtain some properties of the Frattini p-subsystem and give the relationship between Фp（T） and Ф（T） for solvable Lie triple systems.
文摘As an important index to measure the degree of entanglement in quantum systems,concurrence plays an important role in practical research.In this paper,we study the concurrence between two qubits in triangular triple quantum dot structure.Through calculation and simulation,it is found that concurrence is mainly affected by the interdot coupling strength t,Coulomb interactionU,temperature T,and electrode coupling G.Through comparative studies with parallel triple quantum dot structures,we demonstrate that the triangular geometry exhibits significantly enhanced concurrence under identical conditions.In addition,under the condition that concurrence exceeds 0.9,the functional relationship between t and U is obtained through simulation,which provides theoretical support for quantum dot regulation under high entanglement.Finally,we demonstrate the feasibility of implementing a three-qubit quantum gate,using the Toffoli gate as a representative example,under the condition that the triangular triple quantum dot system maintains high entanglement.
基金This work was partially supported by the National Natural Science Foundation of China(Grant No.10371002)the Tianyuan Mathematics Foundation of the National Natural Science Foundation of China(Grant No.10526032)the Natural Science Foundation of Universities of Jiangsu Province(Grant No.05KJB110111).
文摘An LPDTS(υ)is a collection of 3(υ-2)disjoint pure directed triple systems on the same set ofυelements.It is showed in Tian's doctoral thesis that there exists an LPDTS(υ)forυ≡0,4(mod 6),υ≥4.In this paper,we establish the existence of an LPDTS(υ)forυ≡1,3(mod 6),υ>3.Thus the spectrum for LPDTS(υ)is completely determined to be the set{υ:υ≡0,1(mod 3),υ≥4}.
基金This work was partially supported by the National Natural Science Foundation of China(Grant No.10671055)Tianyuan Mathematics Foundation of NSFC(Grant No.10526032)the Natural Science Foundation of Universities of Jiangsu Province(Grant No.05KJB110111)
文摘A directed triple system of order v,denoted by DTS(v,λ),is a pair(X,B)where X is a v-set and B is a collection of transitive triples on X such that every ordered pair of X belongs toλtriples of B.An overlarge set of disjoint DTS(v,λ),denoted by OLDTS(v,λ),is a collection{(Y\{y},Ai)}i,such that Y is a(v+1)-set,each(Y\{y},Ai)is a DTS(v,λ)and all Ai's form a partition of all transitive triples of Y.In this paper,we shall discuss the existence problem of OLDTS(v,λ)and give the following conclusion:there exists an OLDTS(v,λ)if and only if eitherλ=1 and v=0,1(mod 3),orλ=3 and v≠2.
文摘In this paper, we first define a doubly transitive resolvable idempotent quasigroup （DTRIQ）, and show that aDTRIQ of order v exists if and only ifv ≡0（mod3） and v ≠ 2（mod4）. Then we use DTRIQ to present a tripling construction for large sets of resolvable directed triple systems, which improves an earlier version of tripling construction by Kang （J. Combin. Designs, 4 （1996）, 301-321）. As an application, we obtain an LRDTS（4·3^n） for any integer n ≥ 1, which provides an infinite family of even orders.
基金Supported by the National Natural Science Foundation of China(No.10971051 and 11071056)
文摘A hybrid triple system of order v and index A, denoted by HTS（v, λ）, is a pair （X,B） where X is a v-set and B is a collection of cyclic triples and transitive triples on X, such that every ordered pair of X belongs to A triples of B. An overlarge set of disjoint HTS（v, λ）, denoted by OLHTS（v, λ）, is a collection {（Y／{y}, .Ai）}i, such that Y is a （v ＋ 1）-set, each （Y／{y}, Ai） is an HTS（v, λ,） and all Ais form a partition of all cyclic triples and transitive triples on Y. In this paper, we shall discuss the existence problem of OLHTS（v, A） and give the following conclusion： there exists an OLHTS（v, λ） if and only if λ= 1, 2, 4, v = 0, 1 （rood 3） and v ≥ 4.
基金Supported by National Natural Science Foundation of China (Grant No.10771051)
文摘A Mendelsohn triple system of order v （MTS（v）） is a pair （X,B） where X is a v-set and 5g is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of B. An MTS（v） （X,B） is called pure and denoted by PMTS（v） if （x, y, z） ∈ B implies （z, y, x） ∈B. A large set of MTS（v）s （LMTS（v）） is a collection of v - 2 pairwise disjoint MTS（v）s on a v-set. A self-converse large set of PMTS（v）s, denoted by LPMTS＊ （v）, is an LMTS（v） containing [ v-2/2] converse pairs of PMTS（v）s. In this paper, some results about the existence and non-existence for LPMTS＊ （v） are obtained.
基金supported by National Natural Science Foundation of China(Grant Nos.10971051,10701060,10831002)Qing Lan Project of Jiangsu Province,China
文摘A family(X,B1),(X,B2),...,(X,Bq)of q STS(v)s is aλ-fold large set of STS(v)and denoted by LSTSλ(v)if every 3-subset of X is contained in exactlyλSTS(v)s of the collection.It is indecomposable and denoted by IDLSTSλ(v)if there exists no LSTSλ(v)contained in the collection for anyλ【λ.In 1995,Griggs and Rosa posed a problem:For which values ofλ】1 and orders v≡1,3(mod 6)do there exist IDLSTSλ(v)?In this paper,we use partitionable candelabra systems(PCSs)and holeyλ-fold large set of STS(v)(HLSTSλ(v))as auxiliary designs to establish a recursive construction for IDLSTSλ(v)and show that there exists an IDLSTSλ(v)forλ=2,3,4 and v≡1,3(mod 6).
基金supported by NSFC Grant 10671055NSFHB A2007000230Foundation of Hebei Normal University L2004Y11, L2007B22
文摘In this paper, we introduce a new concept -- overlarge sets of generalized Kirkman systems （OLGKS）, research the relation between it and OLKTS, and obtain some new results for OLKTS. The main conclusion is： If there exist both an OLKF（6^k） and a 3-OLGKS（6^k-1,4） for all k ∈{6,7,...,40}／{8,17,21,22,25,26}, then there exists an OLKTS（v） for any v ≡ 3 （mod 6）, v ≠ 21. As well, we obtain the following result： There exists an OLKTS（6u ＋ 3） for u = 2^2n-1 - 1, 7^n, 31^n, 127^n, 4^r25^s, where n ≥ 1,r＋s≥ 1.
