| 行和列和为常量的(0,1)-矩阵的计数 |
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| 引用本文： | 谭中华,高山珍.行和列和为常量的(0,1)-矩阵的计数[J].高校应用数学学报(英文版),2006,21(4):479-486. |
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| 作者姓名： | 谭中华 高山珍 |
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| 作者单位： | Dept.of Math.Sci. |
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| 摘 要： | Let fs,t(m,n) be the number of (0,1) - matrices of size m x 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 CombinatoricsⅠ(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.
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| 关 键 词： | （0 1）矩阵 发生函数 递归公式 常量 |
| 收稿时间： | 2005-05-23 |
| 修稿时间： | 2006-02-17 |
Enumeration of (0,1)-matrices with constant row and column sums |
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| Zhonghua Tan,Shanzhen Gao,Niederhausen Heinrich.Enumeration of (0,1)-matrices with constant row and column sums[J].Applied Mathematics A Journal of Chinese Universities,2006,21(4):479-486. |
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| Authors: | Zhonghua Tan Shanzhen Gao Niederhausen Heinrich |
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| Institution: | 1. Dept. of Appl. Math., Guangdong Univ. of Tech., Guangzhou, 510090, China
2. Dept. of Math. Sci., Florida Atlantic Univ., Boca Raton, FL, 33431, USA
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| Abstract: | Let f s,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 f s,t(m,n)? As R. P. Staneley has observed (Enumerative Combinatorics I (1997), Example 1.1.3), the determination of f s,t(m,n) is an unsolved problem, except for very small s,t. In this paper the closed formulas for f 2,2(n,n), f 3,2(m,n), f 4,2(m,n) are given. And recursion formulas and generating functions are discussed. |
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| Keywords: | (0 1)-matrices labelled ball arrangement generating function |
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