Polynomial argument for $q$-binomial cubic sums*

Factors of alternating sums of products of binomial and q-binomial coefficients

In this paper we study the factors of some alternating sums of products of binomial and q-binomial coefficients. We prove that for all positive integers

Chromatic Polynomial, Colored Jones Function and Q-binomial Counting

Abstract. We define a q-chromatic function on graphs, list some of its properties and provide some formulas in the class of general chordal graphs. Then we relate the q-chromatic function to the colored Jones function of knots. This leads to a curious expression of the colored Jones function of a knot diagram K as a ’defected chromatic operator’ applied to a power series whose coefficients are ...

Binomial Sums and Identities

Generalising Tuenter’s binomial sums

Tuenter [Fibonacci Quarterly 40 (2002), 175-180] and other authors have considered centred binomial sums of the form Sr(n) = ∑

Multiple binomial sums

Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with algebraic generating function. We study the representation of the generating functions of binomial sums by integrals of rational functions. The outcome is two...