Related papers: New proofs of Melzak's identity
Recently, Pankaj Jyoti Mahanta and Manjil P. Saikika proved some identities relating certain restricted partitions into distinct odd parts with the partition whose odd parts are distinct combinatorially. They asked for the q-series proofs.…
A probability method is provided to prove three classes of combinatorial identities. The method is extremely simple, only one step after the proper probability setup.
The aim of this paper is to give identities which are generalizations of the formulas given by Koornwinder [J. Math. Phys. 30, (1989)] and Hamdi-Zeng [J. Math. Phys. 51, (2010)]. Our proofs are much simpler than and different from the…
We prove some combinatorial identities using the Polya urn and the closely related Hoppe urn.
A paper of the first author and Zilke proposed seven combinatorial problems around formulas for the characteristic polynomial and the exponents of an isolated quasihomogeneous singularity. The most important of them was a conjecture on the…
In this note, we find a combinatorial identity which is closely related to the multi-dimensional integral $\gamma_{m}$ in the study of divisor functions. As an application, we determine the finite dual of the group algebra of infinite…
In 1998, Borwein, Bradley, Broadhurst and Lison\v{e}k posed two families of conjectural identities among multiple zeta values, later generalized by Charlton using his alternating block notation. In this paper, we prove a new class of…
The original Beck conjecture, now a theorem due to Andrews, states that the difference in the number of parts in all partitions into odd parts and the number of parts in all strict partitions is equal to the number of partitions whose set…
In this paper, we study some properties of associated sequaences in umbral calculus. From these properties, we derive new and interesting identities of several kinds of polynomials.
We present a method for proving q-series identities by combinatorial telescoping, in the sense that one can transform a bijection or a classification of combinatorial objects into a telescoping relation. We shall illustrate this method by…
In a recent paper, Griffin, Ono and Warnaar present a framework for Rogers-Ramanujan type identities using Hall-Littlewood polynomials to arrive at expressions of the form \[\sum_{\lambda : \lambda_1 \leq m}…
We give a combinatorial proof via a sign-reversing involution for a new identity that generalizes both the Hockey Stick Identity and the Big Hockey Stick and Pucks Identity.
Recently, George Andrews has given a Glaisher style proof of a finite version of Euler's partition identity. We generalise this result by giving a finite version of Glaisher's partition identity. Both the generating function and bijective…
In this note, using Cluckers-Loeser's theory of motivic integration, we prove the integral identity conjecture with framework a localized Grothendieck ring of varieties over an arbitrary base field of characteristic zero.
In this paper, we give a short proof of a relation generalizing many identities for Bernoulli numbers.
For a fixed odd prime $\ell$, we present new families of identities defined on various subposets of the poset of isomorphism classes of finite abelian $\ell$-groups, generalizing identities of Hall and Cohen-Lenstra. We also present a…
In this paper, we obtain a generalization of an identity due to Carlitz on Bernoulli polynomials. Then we use this generalized formula to derive two symmetric identities which reduce to some known identities on Bernoulli polynomials and…
This paper presents a new family of almost identities. These are based on series that sum to elements close to either rationals or rational multiples of pi. The explanation of the phenomenon takes its roots in the theory of Mellin…
We present a new proof for the main claim made in the author's paper "On the identity bases of Brandt semigroups" (Ural. Gos. Univ. Mat. Zap. 14, no.1 (1985), 38--42); this claim provides an identity basis for an arbitrary Brandt semigroup…
In this paper we give a combinatorial proof and refinement of a Rogers-Ramanujan type partition identity of Siladi\'c arising from the study of Lie algebras. Our proof uses generating functions and $q$-difference equations.