Stirling数关于3的一个整除性质(英文)

A divisibility property by 3 for Stirling numbers

在本文中,作者主要研究了第二类Stirling数S(n,k)及其差的3-adic赋值.设m,n为正整数且n≥m≥4.作者证明了ν_3(S(3^(n+1),3~m)-S(3~n,3~m))=n-m+3.

In this paper, the author investigates the 3-adic valuations of the Stirling numbers S（n,k） of the second kind and their differences. The author show that u3 （S（3n＋1, 3m） -S（3n, 3m）） = n -m ＋ 3 for any positive integers n ≥ m≥ 4.