In this paper we give combinatorial proofs of two recurrence relations for the special class of objects known as inplace compositions. We also obtain new identities for the numbers of inplace 1-2 compositions and pali...In this paper we give combinatorial proofs of two recurrence relations for the special class of objects known as inplace compositions. We also obtain new identities for the numbers of inplace 1-2 compositions and palindromic compositions.展开更多
In this paper, we study the palindromic compositions of even integers when no 2＇s are allowed in a composition and its conjugate. We show that the number of these palindromes is equal to 2Fn-1, where, Fn is the n-th ...In this paper, we study the palindromic compositions of even integers when no 2＇s are allowed in a composition and its conjugate. We show that the number of these palindromes is equal to 2Fn-1, where, Fn is the n-th Fibonacci number. Consequently, we obtain several identities between the number of these palindromes, the number of compositions into parts equal to 1＇s or 2＇s, the number of compositions into odd parts and the number of compositions into parts greater than 1.展开更多
A graph is introduced,which allows of a combinatorial interpretation of a discrete-timesemi-infinite Lotka-Volterra (dLV) equation.In particular,Hankel determinants used in a determinantsolution to the dLV equation ar...A graph is introduced,which allows of a combinatorial interpretation of a discrete-timesemi-infinite Lotka-Volterra (dLV) equation.In particular,Hankel determinants used in a determinantsolution to the dLV equation are evaluated,via the Gessel-Viennot method,in terms of non-intersectingsubgraphs.Further,the recurrence of the dLV equation describing its time-evolution is equivalentlyexpressed as a time-evolution of weight of specific subgraphs.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11461020)
文摘In this paper we give combinatorial proofs of two recurrence relations for the special class of objects known as inplace compositions. We also obtain new identities for the numbers of inplace 1-2 compositions and palindromic compositions.
基金Supported by the National Natural Science Foundation of China(Grant No.11461020)
文摘In this paper, we study the palindromic compositions of even integers when no 2＇s are allowed in a composition and its conjugate. We show that the number of these palindromes is equal to 2Fn-1, where, Fn is the n-th Fibonacci number. Consequently, we obtain several identities between the number of these palindromes, the number of compositions into parts equal to 1＇s or 2＇s, the number of compositions into odd parts and the number of compositions into parts greater than 1.
文摘A graph is introduced,which allows of a combinatorial interpretation of a discrete-timesemi-infinite Lotka-Volterra (dLV) equation.In particular,Hankel determinants used in a determinantsolution to the dLV equation are evaluated,via the Gessel-Viennot method,in terms of non-intersectingsubgraphs.Further,the recurrence of the dLV equation describing its time-evolution is equivalentlyexpressed as a time-evolution of weight of specific subgraphs.
