最大跳跃数M(19,10)

北京邮电大学学报

最大跳跃数M(19,10)

1.大连理工大学应用数学系,大连 116023;2.海南师范大学组合与信息实验室,海口 571158

基金资助:
海南省自然科学基金(10002)；

The Maximal Jump Number M(19,10)

1.Department of Applied Mathematics, Dalian University of Technology, Dalian 116023, China; 2.Combinatorics and Information Laboratory, Hainan Normal University, Haikou 571158, China

摘要/Abstract

摘要： 如果n及k（n≥k）是两个较大的正整数,那么要计算出最大跳跃数M（n,k）的值非常困难,Brualdi与Jung曾给出了当1≤k≤n≤10时M（n,k）的值,对于k=10,n=19,证明了M（19,10）=33,这证实了Brualdi与Jung的关于最大跳跃数M（2k+1,k+1）的值的猜想在k=9时成立,但是他们的另一个猜想M（n,k）

关键词: (0,1)-矩阵, 最大跳跃数, 猜想

Abstract: If n and k (n>=k) are two large positive integers, then it is quite difficult to give the value of the maximal jump number M(n,k). Brualdi and Jung gave a table about the values of M(n,k) for 1<=k<=n<=10. For k=10, n=19, we prove M(19,10)=33, which verifies that one of their conjecture about the value M(2k+1,k+1) holds for k=9 and that their another conjecture M(n,k)

Key words: (0,1)-matrix, maximal jump number, conjecture

中图分类号:

O153.1

游林1,2,王天明1. 最大跳跃数M(19,10)[J]. 北京邮电大学学报.

YOU Lin1,2, WANG Tian-ming1. The Maximal Jump Number M(19,10)[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM.