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Prime Power Divisors of Multinomial and q-Multinomial Coefficients

✍ Scribed by Grigori Kolesnik

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 151 KB
Volume: 89
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2001.2657

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✦ Synopsis

We prove that for any integer d multinomial coefficients satisfying some conditions are exactly divisible by p d for many large primes p. The obtained results are essentially the best possible. Also, we show that under some hypothesis q-multinomial coefficients are divisible by p d .

2001 Academic Press

Theorem A is a simple corollary of related results on divisibility of binomial coefficients and we improved it in [1]. Here we further improve it in Theorems 1 4.

Since the case k=2 was studied in [1], we assume that k>2.

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