On Divisibility of Convolutions of Central Binomial Coefficients

On 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.

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...

ON 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...

Additions and Corrections "M.H.Alamatsaz- On Modality and Divisibility of Poisson and Binomial Mixtures. J.Sci. I.R. Iran, Vol.l,No.3, Spring 1990

Factors of sums of powers of binomial coefficients

We prove divisibility properties for sums of powers of binomial coefficients and of q-binomial coefficients. Dedicated to the memory of Paul Erdős