The class of generalized α-matrices is presented by Cvetkovi?, L. (2006), and proved to be a subclass of H-matrices. In this paper, we present a new class of matrices-generalized irreducible α-matrices, and prove th...The class of generalized α-matrices is presented by Cvetkovi?, L. (2006), and proved to be a subclass of H-matrices. In this paper, we present a new class of matrices-generalized irreducible α-matrices, and prove that a generalized irreducible α-matrix is an H-matrix. Furthermore, using the generalized arithmetic-geometric mean inequality, we obtain two new classes of H-matrices. As applications of the obtained results, three regions including all the eigenvalues of a matrix are given.展开更多
Let fs,t（m, n） be the number of （0, 1） - matrices of size m × n such that each row has exactly s ones and each column has exactly t ones （sm = nt）. How to determine fs,t（m,n）？ As R. P. Stanley has obser...Let fs,t（m, n） be the number of （0, 1） - matrices of size m × n such that each row has exactly s ones and each column has exactly t ones （sm = nt）. How to determine fs,t（m,n）？ As R. P. Stanley has observed （Enumerative Combinatorics I （1997）, Example 1.1.3）, the determination of fs,t（m, n） is an unsolved problem, except for very small s, t. In this paper the closed formulas for f2,2（n, n）, f3,2（m, n）, f4,2（m, n） are given. And recursion formulas and generating functions are discussed.展开更多
In 1992, Brualdi and Jung first introduced the maximum jump number M(n, k), that is, the maximum number of the jumps of all (0, 1)-matrices of order n with k 1's in each row and column, and then gave a table about...In 1992, Brualdi and Jung first introduced the maximum jump number M(n, k), that is, the maximum number of the jumps of all (0, 1)-matrices of order n with k 1's in each row and column, and then gave a table about the values of M(n, k) when 1 ≤ k ≤ n ≤ 10. They also put forward several conjectures, including the conjecture M(2k - 2, k) = 3k - 4 + [k-2/2]. In this paper, we prove that b(A) ≥ 4 for every A ∈ A(2k - 2, k) if k ≥ 11, and find another counter-example to this conjecture .展开更多
The maxinmum jump number M(n, k) over a class of n×n matrices of zerosand ones with constant row and column sum k has been investigated by Brualdi andJung in [1] where they proposed the conjectureM(2k, k + 1) = 3...The maxinmum jump number M(n, k) over a class of n×n matrices of zerosand ones with constant row and column sum k has been investigated by Brualdi andJung in [1] where they proposed the conjectureM(2k, k + 1) = 3l - 1 + [k-1/2]In this note, we give two counter-examples to this conjecture.展开更多
文摘The class of generalized α-matrices is presented by Cvetkovi?, L. (2006), and proved to be a subclass of H-matrices. In this paper, we present a new class of matrices-generalized irreducible α-matrices, and prove that a generalized irreducible α-matrix is an H-matrix. Furthermore, using the generalized arithmetic-geometric mean inequality, we obtain two new classes of H-matrices. As applications of the obtained results, three regions including all the eigenvalues of a matrix are given.
文摘Let fs,t（m, n） be the number of （0, 1） - matrices of size m × n such that each row has exactly s ones and each column has exactly t ones （sm = nt）. How to determine fs,t（m,n）？ As R. P. Stanley has observed （Enumerative Combinatorics I （1997）, Example 1.1.3）, the determination of fs,t（m, n） is an unsolved problem, except for very small s, t. In this paper the closed formulas for f2,2（n, n）, f3,2（m, n）, f4,2（m, n） are given. And recursion formulas and generating functions are discussed.
基金Hainan Natural Science Foundation of Hainan (10002)
文摘In 1992, Brualdi and Jung first introduced the maximum jump number M(n, k), that is, the maximum number of the jumps of all (0, 1)-matrices of order n with k 1's in each row and column, and then gave a table about the values of M(n, k) when 1 ≤ k ≤ n ≤ 10. They also put forward several conjectures, including the conjecture M(2k - 2, k) = 3k - 4 + [k-2/2]. In this paper, we prove that b(A) ≥ 4 for every A ∈ A(2k - 2, k) if k ≥ 11, and find another counter-example to this conjecture .
基金Supported by the Science Foundation of Hainan(10002)
文摘The maxinmum jump number M(n, k) over a class of n×n matrices of zerosand ones with constant row and column sum k has been investigated by Brualdi andJung in [1] where they proposed the conjectureM(2k, k + 1) = 3l - 1 + [k-1/2]In this note, we give two counter-examples to this conjecture.
