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Force-responsive symmetric cell divisions orient stomata along global tissue axes. [PDF]

Proc Natl Acad Sci U S A
Hartman KS, Lopez BY, Gonzalez JH, Goetz ME, Cleveland A, Muroyama A.   +5 more
europepmc   +1 more source

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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Skew-Symmetric Differential Operatorsand Combinatorial Identities

Monatshefte Fur Mathematik, 1999
In this paper, we classify all one-function skew-symmetric and super skew-symmetric differential operators by four combinatorial identities related to hyperbolic ...
Xu, XP
exaly   +1 more source

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Words Separation and Positive Identities in Symmetric Groups

J. Autom. Lang. Comb., 2021
Journal of Automata, Languages and Combinatorics, Volume 26, Numbers 1-2, 2021, 67 ...
Olga Karpova, Arseny M. Shur
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Identities of symmetric and skew-symmetric matrices in characteristicp

Rendiconti del Circolo Matematico di Palermo, 1995
This paper is related to the Konstant-Rowen extension to skew-symmetric matrices of the Amitsur-Levitzki identity. A general method is provided, based on a graph theoretic approach, for deriving extensions of known permanental-type identities to skew-symmetric and symmetric matrices over a commutative ring of prime characteristic.
Révész, Gábor, Szigeti, Jenő
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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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A symmetric generalization of an identity of Andrews and Yee

Discrete Mathematics, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Victor J. W. Guo, Su-Dan Wang
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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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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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