Asymptotic prime-power divisibility of binomial, generalized binomial, and multinomial coefficients
نویسندگان
چکیده
منابع مشابه
On Divisibility concerning Binomial Coefficients
Binomial coefficients arise naturally in combinatorics. Recently the speaker initiated the study of certain divisibility properties of binomial coefficients, and products or sums of binomial coefficients. In this talk we introduce the speaker’s related results and various conjectures. The materials come from the author’s two preprints: 1. Z. W. Sun, Products and sums divisible by central binomi...
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This paper, using computational and theoretical methods, deals with prime divisors of binomial coefficients: Geometric distribution and number of distinct prime divisors are studied. We give a numerical result on a conjecture by Erdôs on square divisors of binomial coefficients.
متن کاملOn the Prime Factorization of Binomial Coefficients
For positive integers n and k, with n>-2k, let (k) = uv, where each prime factor of u is less than k, and each prime factor of v is at least equal to k. It is shown that u < v holds with just 12 exceptions, which are determined . If (k) = UV, where each prime factor of U is at most equal to k, and each prime factor of V is greater than k, then U< V holds with at most finitely many exceptions, 1...
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Some structural aspects of mixtures, in general, have been previously investigated by the author in [I] and [2]. The aim of this article is to investigate some important structural properties of the special cases of Poisson and binomial mixtures in detail. Some necessary and sufficient conditions are arrived at for different modality and divisibility properties of a Poisson mixture based o...
متن کاملOn Divisibility of Convolutions of Central Binomial Coefficients
Recently, Z. Sun proved that 2 (2m + 1) ( 2m m ) | ( 6m 3m )( 3m m ) for m ∈ Z>0. In this paper, we consider a generalization of this result by defining bn,k = 2k (n + 2k − 2)!! (n− 2)!! k! . In this notation, Sun’s result may be expressed as 2 (2m + 1) | b(2m+1),(2m+1)−1 for m ∈ Z>0. In this paper, we prove that 2n | bn,un±2r for n ∈ Z>0 and u, r ∈ Z>0 with un ± 2r > 0. In addition, we prove a...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1997
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-97-01794-7