Related papers: Proof of a partition identity conjectured by Lassa…

In this paper, we proved a special case of the DDVV Conjecture.

A special case of an elegant result due to Anderson proves that the number of $(s,s+1)$-core partitions is finite and is given by the Catalan number $C_s$. Amdeberhan recently conjectured that the number of $(s,s+1)$-core partitions into…

We give "hybrid" proofs of the $q$-binomial theorem and other identities. The proofs are "hybrid" in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the…

Arthur's conjectures predict the existence of some very interesting unitary representations occurring in spaces of automorphic forms. We prove the unitarity of the "Langlands element" (i.e., the one specified by Arthur) of all unipotent…

This paper provides algebraic proofs for several types of congruences involving the multipartition function and self-convolutions of the divisor function. Our computations use methods of Differential Algebra in $\mathbb{Z}/q\mathbb{Z}$,…

In most text books on number theory Wilson Theorem is proved by applying Lagrange theorem concerning polynomial congruences.Hardy and Wright also give a proof using cuadratic residues. In this article Wilson theorem is derived as a…

A proof is given of Rosenthal's \(\ell_1\) theorem.

In this note we show through infinitary derivations that each provably well-founded strict partial order in ${\rm ACA}_{0}$ admits an embedding to an ordinal$<\varepsilon_{0}$.

We prove a conjecture of Johann Cigler on shifted Hankel determinants.

An identity that is reminiscent of the Littlewood identity plays a fundamental role in recent proofs of the facts that alternating sign triangles are equinumerous with totally symmetric self-complementary plane partitions and that…

A $\lambda$-calculus is introduced in which all programs can be evaluated in probabilistic polynomial time and in which there is sufficient structure to represent sequential cryptographic constructions and adversaries for them, even when…

The theory of partition congruences has been a fascinating and difficult subject for over a century now. In attempting to prove a given congruence family, multiple possible complications include the genus of the underlying modular curve,…

New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.

We give a simple proof of the Lalonde-McDuff conjecture for aspherical manifolds.

This paper is an extension program of the notion of circle of partition developed in our first paper \cite{CoP}. As an application we prove the Erd\H{o}s-Tur\'{a}n additive base conjecture.

We give new proofs of MacMahon and Russell's modulo 6 identities using the method of weighted words. We also present a new refinement of MacMahon's identity, some related finite sum identities, and a companion partition theorem to sequence…

We show that a proof in multiplicative linear logic can be represented as a decorated surface, such that two proofs are logically equivalent just when their surfaces are geometrically equivalent. This is an extended abstract for…

In this work it is propose an alterative proof of one of basic properties of the zonal polynomials. This identity is generalised for the Jack polynomials.

We present proofs of two new families of sum-product identities arising from the cylindric partitions paradigm. Most of the presented expressions, the related sum-product identities, and the ingredients for the proofs were first conjectured…

We consider several examples of probabilistic existence proofs using compressibility arguments, including some results that involve Lov\'asz local lemma.