Vol. 50, No. 1, 1974

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ISSN: 0030-8730
The numer of multinomial coefficients divisible by a fixed power of a prime

Frederic Timothy Howard

Vol. 50 (1974), No. 1, 99–108

In this paper some results of L. Carlitz and the writer concerning the number of binomial coefficients divisible by pj but not by pj+1 are generalized to multinomial coefficients. In particular 𝜃j(k;n) is defined to be the number of multinomial coefficients n|[n1,,nk] divisible by exactly pj, and formulas are found for 𝜃j(k;n) for certain values of j and n. Also the generating function technique used by Carlitz for binomial coefficients is generalized to multinomial coefficients.

Mathematical Subject Classification 2000
Primary: 10A25
Secondary: 05A10
Received: 11 September 1972
Published: 1 January 1974
Frederic Timothy Howard