On the Number of Distinct Multinomial Coefficients

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dc.creatorAndrews, George E.
dc.creatorKnopfmacher, Arnold
dc.creatorZimmermann, Burkhard
dc.date2005-09-21
dc.date.accessioned2026-07-07T06:29:31Z
dc.date.available2026-07-07T06:29:31Z
dc.descriptionWe 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.
dc.description16 pages, to be published in the Journal of Number Theory
dc.identifierhttps://arxiv.org/abs/math/0509470
dc.identifierhttp://arxiv.org/abs/math/0509470
dc.identifierJournal of Number Theory, Volume 118, Issue 1, May 2006, Pages 15-30
dc.identifierdoi:10.1016/j.jnt.2005.08.012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98057
dc.subjectCombinatorics
dc.subjectCommutative Algebra
dc.subject05A10, 05A17 (Primary), 13P10 (Secondary)
dc.titleOn the Number of Distinct Multinomial Coefficients
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