Reducing multinomial coefficients modulo a prime power
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.
scientific article; zbMATH DE number 3855199