On the Number of Distinct Multinomial Coefficients

Andrews, George E.; Knopfmacher, Arnold; Zimmermann, Burkhard

On the Number of Distinct Multinomial Coefficients

Authors

Andrews, George E.

Knopfmacher, Arnold

Zimmermann, Burkhard

Description

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