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: [email protected] (G.E. Andrews), [email protected] (A. Knopfmacher), [email protected] (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.
UR - https://www.scopus.com/pages/publications/33645946053
UR - https://www.scopus.com/pages/publications/33645946053#tab=citedBy
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 -