On the number of distinct multinomial coefficients

George E. Andrews, Arnold Knopfmacher, Burkhard Zimmermann

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)15-30
Number of pages16
JournalJournal of Number Theory
Volume118
Issue number1
DOIs
StatePublished - May 1 2006

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Multinomial Coefficients
Partition
Distinct
Commutative Algebra
Infinity
Tend
Zero

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Andrews, George E. ; Knopfmacher, Arnold ; Zimmermann, Burkhard. / On the number of distinct multinomial coefficients. In: Journal of Number Theory. 2006 ; Vol. 118, No. 1. pp. 15-30.
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On the number of distinct multinomial coefficients. / Andrews, George E.; Knopfmacher, Arnold; Zimmermann, Burkhard.

In: Journal of Number Theory, Vol. 118, No. 1, 01.05.2006, p. 15-30.

Research output: Contribution to journalArticle

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AB - 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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