多元多项式指数和的可除性(英文)

On the Divisibility of Multinomial Exponent Sums

对任意正整数m,n,r,定义S_(n,m)^((r))=Σ_(k_1+K_2+…+k_m=n)(_(k_1,k_2,…,k_m)~n)~r,并定义T_(n,m)^((r))=Σ_(k_1+K_2+…+k_m=n)(-1)^(k_1)(_(k_1,k_2,…,k_m)~n)~r.对S_(n,m)^((r))和T_(n,m)^((r))获得了若干可除性性质.

n r Abstract： For any positive integers m, n, r, define S^r/n,m=Σ_（k1＋K2＋…＋km=n）（k1,k2,^n…,km）^r, T^r/n,m=Σ_（k1＋K2＋…＋km=n）（-1）^k1（k1,k2,^n…,km）^r.In this paper, we obtain several divisible proper-ties on S^r/n,m and T^r/n,m