Related papers: An analogue to the Witt identity

In a Hom-Malcev algebra an identity, equivalent to the Hom-Malcev identity, is found.

An identity involving symmetric sums of regularized multiple zeta-star values of harmonic type was proved by Hoffman. In this paper, we prove an identity of shuffle type. We use Bell polynomials appearing in the study of set partitions to…

We give a new proof of Chan's identity involving the cubic partition function and we also give a new identity for the cubic partition function which is analogues to the Zuckerman's identity for the ordinary partition function.

We present an identity which can be regarded as a Pfaffian-Hafnian analogue of Borchardt's identity and as a generalization of Schur's identity. We give a proof using the complex analysis.

We derive a combinatorial identity which is useful in studying the distribution of Fourier coefficients of L-functions by allowing us to pass from knowledge of moments of the coefficients to the distribution of the coefficients.

In this paper we prove some combinatorial identities which can be considered as generalizations and variations of remarkable Chu-Vandermonde identity. These identities are proved by using an elementary combinatorial-probabilistic approach…

We prove a new general differential identity and an associated integral identity, which entails a pair of solutions of the Poisson equation with constant source term. This generalizes a formula that the first and third authors previously…

Some applications of a result, which is proved recently, is considered. We first prove three determinantal identities concerning the binomial coefficient and Stirling numbers of the first and the second kind. We also easily obtain the…

We prove two multivariate $q$-binomial identities conjectured by Bousseau, Brini and van Garrel [Geom. Topol. 28 (2024), 393-496, arXiv:2011.08830] which give generating series for Gromov-Witten invariants of two specific log Calabi-Yau…

In this article we explore some of the combinatorial consequences of recent results relating the isospectral commuting variety and the Hilbert scheme of points in the plane.

We construct a new equivariant cohomology theory for a certain class of differential vertex algebras, which we call the chiral equivariant cohomology. A principal example of a differential vertex algebra in this class is the chiral de Rham…

We prove an analogue to the Cayley identity for an arbitrary self-adjoint operator in a Hilbert space. We also provide two new ways to characterize vectors belonging to the singular spectral subspace in terms of the analytic properties of…

We describe all Witt invariants of anti-hermitian forms over a quaternion algebra with its canonical involution, and in particular all Witt invariants of orthogonal groups $O(A,\sigma)$ where $(A,\sigma)$ is an central simple algebra with…

In this article, we prove a new general identity involving the Theta operators introduced by the first author and his collaborators in [D'Adderio, Iraci, Vanden Wyngaerd 2020]. From this result, we can easily deduce several new identities…

Let $A$ be a finite-dimensional (Artinian) Gorenstein algebra, and let $\operatorname{Aut}(A)^{\circ}$ denote the connected component of the identity in the automorphism group of $A$. We introduce a new subclass of Gorenstein algebras and…

We exhibit an identity that plays the same role as Vaughan's identity but is arguably simpler

Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are…

In the case of quadratic forms over a field, it is well-known that the prime spectrum of the Witt ring and the space of orderings of the field determine one another, through associated signature maps. We show that a sililar relation holds…

We generalise the signed Bollobas-Riordan polynomial of S. Chmutov and I. Pak [Moscow Math. J. 7 (2007), no. 3, 409-418] to a multivariate signed polynomial Z and study its properties. We prove the invariance of Z under the recently defined…

In this papier, by the classical umbral calculus method, we establish identities involving the Appell polynomials and extend some existing identities.