On divisibility of binomial 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...
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...
متن کاملON MODALITY AND DIVISIBILITY OF POISSON AND BINOMIAL MIXTURES
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 Properties of Some Differences of the Central Binomial Coefficients and Catalan Numbers
We discuss divisibility properties of some differences of the central binomial coefficients and Catalan numbers. The main tool is the application of various congruences modulo high prime powers for binomial coefficients combined with some recurrence relevant to these combinatorial quantities.
متن کاملProof of a Conjecture of Amdeberhan and Moll on a Divisibility Property of Binomial Coefficients
Let a, b and n be positive integers with a > b. In this note, we prove that (2bn + 1)(2bn + 3) ( 2bn bn )∣∣∣∣3(a− b)(3a− b)(2an an )( an bn ) . This confirms a recent conjecture of Amdeberhan and Moll.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1994
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)e0104-c