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Multivariate Symmetric Identities

The Fibonacci Quarterly, 1996
Starting from these identities, Gould ([3], [4]) obtained various convolution identities. The multivariate case of (1.2) and (1.4) was obtained by Carlitz [1] using MacMahon's "master theorem." Using other methods, Cohen and Hudson [2] gave bivariate ...
Abdelhamid Abderrezzak
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Pairs of Symmetric and Skew-Symmetric Toeplitz Matrices with Identical Squares

Journal of Mathematical Sciences, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Words Separation and Positive Identities in Symmetric Groups

2021
Journal of Automata, Languages and Combinatorics, Volume 26, Numbers 1-2, 2021, 67 ...
Karpova, Olga, Shur, Arseny M.
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Symmetric Functions and Bijective Identities

1992
Publisher Summary This chapter discusses the concept of symmetric functions and bijective identities. One of the latest interests of Combinatorics is the development of a systematic theory of bijective proofs. In this context, the idea of proving identities among symmetric functions by bijective arguments is recalled.
SENATO PULLANO, Domenico, A. VENEZIA
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Harmonic-number summation identities, symmetric functions, and multiple zeta values

, 2016
We show how infinite series of a certain type involving generalized harmonic numbers can be computed using a knowledge of symmetric functions and multiple zeta values.
Michael E. Hoffman
semanticscholar   +1 more source

The identities of symmetric matrices.

2009
Let $H\sb{n}$ denote the subspace of symmetric matrices of $M\sb{n},$ the full $n\times n$ matrix algebra with coefficients in a field F. Let $$T\sb{2n}(x\sb1,\...,x\sb{2n-1}; x\sb0)=\sum\limits\sb{\sigma\in S\sb{2n-1}\atop i\equiv 1, 2\ mod\ 4} (-1)\sp{\sigma+i-1}x\sb{\sigma(1)}\cdots \sbsp{x\sb0}{(i)}\cdots x\sb{\sigma(2n-1)},$$and $e(n) = n$ if n is
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Two Symmetric Identities Involving Complete and Elementary Symmetric Functions

Bulletin of the Malaysian Mathematical Sciences Society, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Symmetric units and group identities

manuscripta mathematica, 1998
In the paper under review the authors discuss when the set of symmetric units of a group ring satisfies a group identity. A unit of a group algebra is called a symmetric unit if it is stable under the involution coming from the natural Hopf algebra structure of the group ring.
Giambruno, A., Sehgal, S. K., Valenti, A.   +2 more
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Trace identities for skew-symmetric matrices

, 2016
We derive an expression for the product of the Pfaffians of two skew-symmetric matrices A and B as a sum of products of the traces of powers of AB and an expression for the inverse matrix A$^{-1}$, or equivalently B$^{-1}$, as a finite-order polynomial ...
M. Krivoruchenko
semanticscholar   +1 more source

COMMUTATOR IDENTITIES ON SYMMETRIC ELEMENTS OF GROUP ALGEBRAS

Journal of Algebra and Its Applications, 2013
Let K be a field of odd characteristic p, and let G be the direct product of a finite p-group P ≠ 1 and a Hamiltonian 2-group. We show that the set of symmetric elements (KG)* of the group algebra KG with respect to the involution of KG which inverts all elements of G, satisfies all Lie commutator identities of degree t(P) or more, where t(P) denotes ...
Juhász, Tibor, Tóth, Enikő
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