(0,1)-矩阵类u(R,S)的基数函数f(R,S)及其非零集

Cardinal Function f(R S) of the Class u(R S) of(0,l)-Matrices and its Nonzero-point Set

中文摘要:

      

英文摘要:

      Let R and S be two vectors with m and n nonnegative integers as conponents respectively. Let u(R, S) be the class consisting of all m×n (0,1) - matrices with row sum vector R and column sum vector S. Suppose that A is the maximal mrixat with row sum vector R. Let S he the column sum vector of A. (of. H. J. Ryser, Combinatorial Mathematics, Carcus Math. Monograph 14 (1963)). Let L(S)={S=(s₁,…,s_m),S-1≥s₂≥…≥s_n}, and let F(R, S) be the cardinal function of u(R,S), i. e.. f(R, S) = |u(R, S) |. Then L(S) is the nonzero-point set of f(R,S). In this paper our principal result is the following.