Reducing multinomial coefficients modulo a prime power
type: Item
instance of: scholarly article
title: Reducing multinomial coefficients modulo a prime power
zbMATH Open document ID: 0538.10002
DOI: 10.1016/0898-1221(84)90084-1
author: Robert J. Martin
author: Gary L. Mullen
publication date: 1984-01-01T00:00:00Z
review text: The authors are concerned with finding whether a given power \(\geq 1\) of a given prime p will or will not divide the multinomial coefficient \(k!/(k_ 1!k_ 2!....k_ t!)\) where k's are positive integers such that \(k_ 1+k_ 2+...+k_ t=k\). The paper gives all that any reader needs to know in connection with this problem. The method of the authors makes the decision depend on the residues of \(k_ i\) modulo powers \(p^ j\) of p where j runs from 1 to h, h being given by the relation \(p^ h\leq k<p^{h+1}\). The reviewer feels that all this is not necessary at all. (2.1) which the authors also use in their proof of Theorem 1, already provides the required information in a straightforward manner.
reviewed by: Hansraj Gupta
Mathematics Subject Classification ID: 11A05
Mathematics Subject Classification ID: 05A10
zbMATH DE Number: 3855199
zbMATH Keywords: divisibility by powers of primes
zbMATH Keywords: multinomial coefficient
MaRDI profile type: Publication
full work available at URL: 0898-1221(84)90084-1
OpenAlex ID: W1991686793
cites work: The distribution of binomial coefficients \(\pmod p\)
cites work: The number of binomial coefficients divisible by a fixed power of a prime
cites work: Binomial Coefficients Modulo a Prime
cites work: Congruence properties of ordinary and q-binomial coefficients
cites work: Number of Odd Binomial Coefficients
cites work: Q3259107
cites work: Formulas for the Number of Binomial Coefficients Divisible by a Fixed Power of a Prime
cites work: The Lattice Point Covering Theorem for Rectangles
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 3855199