Related papers: A combinatorial proof for Cayley's identity

In proof theory the notion of canonical proof is rather basic, and it is usually taken for granted that a canonical proof of a sentence must be unique up to certain minor syntactical details (such as, e.g., change of bound variables). When…

In view of the recent interest in a short proof of the Jacobi identity for the Poisson-brackets, we provide an alternative simple proof for the same. Our derivation is based on the validity of the Leibnitz rule in the context of dynamical…

This is the second combinatorial proof of the compactness theorem for singular from 1977. In fact it gives a somewhat stronger theorem.

We propose a combinatorial interpretation of the coefficient of $q$ in Kazhdan- Lusztig polynomials and we prove it for finite simply-laced Weyl groups.

We consider combinatorial properties of the Mills' ratio, and explore the interplay between a continued fraction expansion for the Mills' ratio, the Laplace polynomials and a new family of combinatorial identities.

A very short, bijective proof, of Touchard's Catalan identity is given, using Dyck paths.

In a recent paper, Amini et al. introduce a general framework to prove duality theorems between special decompositions and their dual combinatorial object. They thus unify all known ad-hoc proofs in one single theorem. While this…

The combinatorial theory for the set of parity alternating permutations is expounded. In view of the numbers of ascents and inversions, several enumerative aspects of the set are investigated. In particular, it is shown that signed Eulerian…

In this paper we extend the notion of Melham sum to the Pell and Pell-Lucas sequences. While the proofs of general statements rely on the binomial theorem, we prove some spacial cases by the known Pell identities. We also give extensions of…

Recently, B\'{e}nyi and the second author introduced two combinatorial interpretations for symmetrized poly-Bernoulli polynomials. In the present study, we construct bijections between these combinatorial objects. We also define various…

We consider certain functional identities on the matrix algebra $M_n$ that are defined similarly as the trace identities, except that the "coefficients" are arbitrary polynomials, not necessarily those expressible by the traces. The main…

Dumont has conjectured a marvellous identity, which generalizes, in particular, the classical results of Lagrange, Gauss, Jacobi and Kronecker on the sums of two, three and four squares. We give a combinatorial proof of Dumont's conjecture.

We correct a common (but mistaken) attribution of the evaluation of the probability integral, usually attributed to Poisson, Gauss, or Laplace.

This article is concerned with a general scheme on how to obtain constructive proofs for combinatorial theorems that have topological proofs so far. To this end the combinatorial concept of Tucker-property of a finite group $G$ is…

The Casas-Alvero conjecture is about interpolation polynomials. There are some partial proofs of it, but there is not any proof in the general case.In this paper we propose three.

This article is an introduction to combinatorics under the axiom of determinacy with a focus on partition properties and infinity Borel codes.

An earlier work of the author's showed that it was possible to adapt the Alekseev-Meinrenken Chern-Weil proof of the Duflo isomorphism to obtain a completely combinatorial proof of the Wheeling isomorphism. That work depended on a certain…

The equation commonly known as Sury's identity is a deceptively simple summation formula that connects the Lucas numbers, Fibonacci numbers, and powers of two. Many authors have given extensions and generalizations over the years; in this…

In this note we give some identities which involve the Mertens function M(n). Our proofs are combinatorial with relatively prime subsets as a main tool.

In this paper we present a combinatorial proof of Selberg's integral formula. We start by giving a bijective proof of a Theorem about the number of topological orders of a certain related directed graph. Selberg's Integral Formula then…