The Maximum Jump Number of (0, 1)-Matrices of Order 2k - 2 with Fixed Row and Column Sum k
Received:May 08, 2002  
Key Words: (0   1)-matrices   jump number   stair number.  
Fund Project:Hainan Natural Science Foundation of Hainan (10002)
Author NameAffiliation
YOU Lin Lab. of Combinatorics and Information Science
Hainan Normal University
Haikou
China 
WANG Tian-ming Dept. of Appl. Math.
Dalian University of Technology
Dalian
China 
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Abstract:
      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 .
Citation:
DOI:10.3770/j.issn:1000-341X.2005.02.006
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