Related papers: A Remark on the Higher Capelli Identities

We give a stack-theoretic proof for some results on families of hyperelliptic curves.

We prove an interesting identity for the sum of determinants, which is a generalization of the sum of a geometric progression. The proof is quite long and a number of other identities are proved along the way. Some of the more elementary…

We prove that the higher signature for any close oriented manifold is a simple-homotopy invariant.

We present two proofs each, all shorter than the original proofs, of two elegant combinatorial identities that came up in the beautiful article arXiv:2010.00077 .

Making use of the theory of infinitesimal canonical transformations, a concise proof is given of Jacobi's identity for Poisson brackets.

We obtain simple proofs of certain inequalites for bivariate means.

Computations in the cohomology of finite groups.

We discuss representations of monogenic functions over very regular groups.

In this note, we present two new identities for derangements. As a corollary, we have a combinatorial proof of the irreducibility of the standard representation of symmetric groups.

We establish a simple identity and using it we find a new proof of a result of Kloosterman.

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

In this note, using the derangement polynomials and their umbral representation, we give another simple proof of an identity conjectured by Lacasse in the study of the PAC-Bayesian machine learning theory.

We prove an identity on a graph analogous to Bochner's identity on a Riemannian manifold. An auxiliary graph called the complete tangent graph intervenes in the term corresponding to Ricci curvature.

This paper highlights three known identities, each of which involves sums over alternating sign matrices. While proofs of all three are known, the only known derivations are as corollaries of difficult results. The simplicity and natural…

I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.

We give a simple statistical proof of a binomial identity, by evaluating the Laplace transform of the maximum of n independent exponential random variables in two different ways. As a by product, we obtain a simple proof of an interesting…

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

A review of Finite Gap Jacobi Matrices.

In this note, we provide a conceptual explanation of a well-known polynomial identity used in algebraic number theory.

On the basis of the generalizations of the Jacobi identity found by the author some identities satisfied by the curvature and torsion of a covariant differentiation are derived. A kind of the generalized covariant differentiation is…