Related papers: A Remark on the Higher Capelli Identities

In this article, a short combinatorial proof of the Capelli's identity is given. It also leads to an easy proof of the Capelli--Cauchy--Binet identity, a more general form of Capelli's identity. With the technique introduced, the Turnbull's…

In this paper, we give a short proof of a relation generalizing many identities for Bernoulli numbers.

Capelli's and Turnbull's classical identities are given elegant combinatorial proofs.

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

In this note, we will give a short proof of an identity for cubic partitions.

In this note we prove two extensions of the Sury's identity.

Given two combinatorial identities proved earlier, a new set of variations of these combinatorial identities is listed and proved with the integral representation method. Some identities from literature are shown to be special cases of…

We prove Capelli type identities which involve the whole universal enveloping algebra $U(gl(n))$ and matrix elements of irreducible representations of the symmetric group. These identities generalize higher Capelli identities for the center…

We prove a curious identity for the Bernoulli numbers.

We formulate several polynomial identities. One side of these identities has a nice simple form. Whereas the other has a form of a polynomial whose coefficients contain binomial coefficients double factorials or (and) rising factorials. The…

The Capelli identities claim $det(A)det(B) = det(AB+correction)$ for certain matrices with noncommutative entries. They have applications in representation theory and integrable systems. We propose new examples of these identities,…

A simple heuristic proof of an integral identity recently derived (Glasser ML 2011 J. Phys. A: Math. Theor. 44 225202) is presented.

A quantum Capelli identity is given on the multiparameter quantum general linear group based on the $(p_{ij}, u)$-condition. The multiparameter quantum Pfaffian of the $(p_{ij}, u)$-quantum group is also introduced and the transformation…

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

We give a new proof of the existence of designs, which is much shorter and gives better bounds.

In a recent paper, Caracciolo, Sokal and Sportiello presented, inter alia, an algebraic/combinatorial proof for Cayley's identity. The purpose of the present paper is to give a "purely combinatorial" proof for this identity; i.e., a proof…

We give a simple characterization of braids that can be unplaited keeping separately their upper ends and their lower ends tied together

An technically interesting proof of a known theorem.

We derive an identity involving Horadam numbers. Numerous new identities as well as those found in the existing literature are subsumed in this single identity.

Using jagged overpartitions, we give three generalizations of a weighted word version of Capparelli's identity due to Andrews, Alladi, and Gordon and present several corollaries.