游林,王天明.具有固定行列和k的阶为2k-2的(0,1)-矩阵的最大跳跃数(英文)[J].数学研究及应用,2005,25(2):244~254 |
具有固定行列和k的阶为2k-2的(0,1)-矩阵的最大跳跃数(英文) |
The Maximum Jump Number of (0, 1)-Matrices of Order 2k - 2 with Fixed Row and Column Sum k |
投稿时间:2002-05-08 |
DOI:10.3770/j.issn:1000-341X.2005.02.006 |
中文关键词: (0 1)-矩阵 跳跃数 |
英文关键词:(0 1)-matrices jump number stair number. |
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中文摘要: |
1992年Brualdi与Jung首次引出了最大跳跃数M(n,k),即每行每列均含k个1的阶为n的(0,1)-矩阵的跳跃数的极大数,给出了满足条件1≤k ≤n ≤10的(0,1)-矩阵的最大跳跃数M(n,k)的一个表,并提出了几个猜想,其中包括猜想M(2k-2,k)=3k-4+[(k-2)/2].本文证明了当k≥11时,对每个A∈∧(2k-2,k)有b(A)≥4.还得到了该猜想的另一个反例. |
英文摘要: |
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 ∈Λ(2k - 2, k) if k ≥ 11, and find another counter-example to this conjecture . |
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