最大跳跃数M(19,10)

The Maximal Jump Number M(19,10)

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)<M(n+l_1,k+l_2)对l_1=1与l_2=1不成立。

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 ) < M( n + l1 , k + l2) does not hold for l1 = 1 and l2 = 1.