Proof of a Conjecture of Amdeberhan and Moll on a Divisibility Property of Binomial Coefficients

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...

Generalized Fibonacci polynomials and Fibonomial coefficients

The focus of this paper is the study of generalized Fibonacci polynomials and Fibonomial coefficients. The former are polynomials {n} in variables s, t given by {0} = 0, {1} = 1, and {n} = s{n−1}+t{n−2} for n ≥ 2. The latter are defined by { n k } = {n}!/({k}!{n−k}!) where {n}! = {1}{2} . . . {n}. These quotients are also polynomials in s, t and specializations give the ordinary binomial coeffi...

A Note on Amdeberhan-Moll’s Conjecture

Recently, Amdeberhan and Moll gave a conjecture on ASM sequences. In this note, we show that this conjecture is not true and we give a new conjecture.

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

A Pretty Binomial Identity

Elementary proofs abound: the first identity results from choosing x = y = 1 in the binomial expansion of (x+y). The second one may be obtained by comparing the coefficient of x in the identity (1 + x)(1 + x) = (1 + x). The reader is surely aware of many other proofs, including some combinatorial in nature. At the end of the previous century, the evaluation of these sums was trivialized by the ...