On the Number of Distinct Multinomial Coefficients
Combinatorics
2007-05-23 v1 Commutative Algebra
Abstract
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.
Cite
@article{arxiv.math/0509470,
title = {On the Number of Distinct Multinomial Coefficients},
author = {George E. Andrews and Arnold Knopfmacher and Burkhard Zimmermann},
journal= {arXiv preprint arXiv:math/0509470},
year = {2007}
}
Comments
16 pages, to be published in the Journal of Number Theory