高校应用数学学报B辑
高校應用數學學報B輯
고교응용수학학보B집
APPLIED MATHEMATICS A JOURNAL OF CHINESE UNIVERSITIES
2006年
4期
479-486
,共8页
谭中华%高山珍%Heinrich Niederhausen
譚中華%高山珍%Heinrich Niederhausen
담중화%고산진%Heinrich Niederhausen
(0,1)-matrices,labelled ball,arrangement,generating function
Let fs,t(m, n) be the number of (0, 1) - matrices of size m × n such that eachrow 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.
