On the Number of Distinct Multinomial Coefficients

Details On the Number of Distinct Multinomial Coefficients On the Number of Distinct Multinomial Coefficients

2005-09-21

arxiv.org/abs/math/0509470v1

Journal of Number Theory, Volume 118, Issue 1, May 2006, Pages 15-30

Mathematics

Combinatorics

16 pages, to be published in the Journal of Number Theory

Scientific paper

10.1016/j.jnt.2005.08.012

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 pP(n)/M(n) and M(n)/p(n) tend to zero as n goes to infinity, where pP(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.

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