Related papers: q-identities of Fu and Lascoux proved by the q-Ric…

We give here direct proof of a recent conjecture of Jauregui and Tsallis about a new representation of Dirac's delta distribution by means of q-exponentials. The proof is based in the use of tempered ultradistributions' theory.

We show that, up to multiplication by a factor $\frac{1}{(cq;q)_{\infty}}$, the weighted words version of Capparelli's identity is a particular case of the weighted words version of Primc's identity. We prove this first using recurrences,…

Recently, Wang and Ma propose a conjecture associated with the possible generalization of Andrews-Warnaar identities. It is confirmed in this paper. As the applications of this conjecture, we prove that a family of series can be expressed…

Some identities that involve the elliptic version of the Cauchy matrices are presented and proved. They include the determinant formula, the formula for the inverse matrix, the matrix product identity and the factorization formula.

We study the existence of the identity L_n^2 -5F_n^2 = 4(-1)^n.

As a by-product of a finite-size Bethe Ansatz calculation in statistical mechanics, Doochul Kim has established, by an indirect route, three mathematical identities rather similar to the conjugate modulus relations satisfied by the elliptic…

The main aim of the present paper is to represent an exact and simple proof for FLT by using properties of the algebra identities and linear algebra.

Binomial versions of the Andrews-Gordon-Bressoud identities are given.

The celebrated quintuple product identity follows surprisingly from an almost-trivial algebraic identity, which is the limiting case of the terminating q-Dixon formula.

We present some new linear, quadratic, cubic and quartic binomial Fibonacci, Lucas and Fibonacci--Lucas summation identities.

We provide bijective proofs of two classic identities that are very simple to prove using generating functions, but surprisingly difficult to prove combinatorially. The problem of finding a bijective proof for the first identity was first…

We prove that the Rubik's cube group can be realized as a Galois group over the rationals.

Kanade and Russell conjectured several Rogers-Ramanujan-type partition identities, some of which are related to level $2$ characters of the affine Lie algebra $A_9^{(2)}$. Many of these conjectures have been proved by Bringmann,…

We present alternative, q-hypergeometric proofs of some polynomial analogues of classical q-series identities recently discovered by Alladi and Berkovich, and Berkovich and Garvan.

We prove a new q-analogue of Nicomachus's Theorem about the sum of cubes and some related results.

We prove two identities of Hall-Littlewood polynomials, which appeared recently in a paper by two of the authors. We also conjecture, and in some cases prove, new identities which relate infinite sums of symmetric polynomials and partition…

We obtain connection coefficients between $q$-binomial and $q$-trinomial coefficients. Using these, one can transform $q$-binomial identities into a $q$-trinomial identities and back again. To demonstrate the usefulness of this procedure we…

In a recent paper by L. Fel two new identities for the degree of syzygies are given. We present an algebraic proof of them, using only basic homological algebra tools. We also extend these results.

We prove an identity about partitions, previously conjectured in the study of shifted Jack polynomials (math.CO/9903020). The proof given is using $\lambda$-ring techniques. It would be interesting to obtain a bijective proof.

We prove some symmetric $q$-congruences.