TY - JOUR

T1 - On the number of distinct multinomial coefficients

AU - Andrews, George E.

AU - Knopfmacher, Arnold

AU - Zimmermann, Burkhard

N1 - Funding Information:
Keywords: Factorials; Binomial coefficients; Combinatorial functions; Partitions of integers; Polynomial ideals; Gröbner bases * Corresponding author. E-mail addresses: andrews@math.psu.edu (G.E. Andrews), arnoldk@cam.wits.ac.za (A. Knopfmacher), zimmermann@risc.uni-linz.ac.at (B. Zimmermann). 1 Partially supported by National Science Foundation Grant DMS-0200047. 2 Partially supported by The John Knopfmacher Center for Applicable Analysis and Number Theory of the University of the Witwatersrand. 3 Supported by SFB grant F1305 of the Austrian FWF.

PY - 2006/5

Y1 - 2006/5

N2 - 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.

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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U2 - 10.1016/j.jnt.2005.08.012

DO - 10.1016/j.jnt.2005.08.012

M3 - Article

AN - SCOPUS:33645946053

SN - 0022-314X

VL - 118

SP - 15

EP - 30

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 1

ER -