On the number of distinct multinomial coefficients

JOURNAL OF NUMBER THEORY

卷:118

Article

Andrews, GE ; Knopfmacher, A ; Zimmermann, B

关键词: factorials;    binomial coefficients;    combinatorial functions;    partitions of integers;    polynomial ideals;    Grobner bases;   

DOI  :  10.1016/j.jnt.2005.08.012

来源: Elsevier

【 摘 要 】

We study M (n), the number of distinct values taken by multinomial coefficients with upper entry n, and some closely related sequences. We show that both p(P)(n)/M(n) and M(n)/p(n) tend to zero as n goes to infinity, where p(P)(n) is the number of partitions of n into primes and p(n) is the total number of partitions of n. To use methods from commutative algebra, we encode partitions and multinomial coefficients as monomials. (C) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

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