猜想M(2k,k+1)=3k-1+[(k-1)/2]的反例(英文)

Counter-Examples to the Conjecture M(2k, k + 1) = 3k - 1 + [(k-1)/2]

英文关键词:jump number  （0  1）-matrices  conjecture  counter-examples

中文摘要:

      Brualdi与Jung在[1]中研究了一类具有固定线和k的n×n矩阵上的最大跳跃数M(n,k),并提出猜想M(2k, k + 1) = 3k - 1 + [(k-1)/2].本文给出了这一猜想的两个反例．

英文摘要:

      The maxinmum jump number M(n, k) over a class of n×n matrices of zerosand ones with constant row and column sum k has been investigated by Brualdi andJung in [1] where they proposed the conjecture M(2k, k + 1) = 3k - 1 + [(k-1)/2]. In this note, we give two counter-examples to this conjecture.