On the number of distinct multinomial coefficients

George E. Andrews, Arnold Knopfmacher, Burkhard Zimmermann

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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
Issue number1
StatePublished - May 2006

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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