Results 21 to 30 of about 15,374,978 (303)
Words and polynomial invariants of finite groups in non-commutative variables [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Let $V$ be a complex vector space with basis $\{x_1,x_2,\ldots,x_n\}$ and $G$ be a finite subgroup of $GL(V)$. The tensor algebra $T(V)$ over the complex is isomorphic to the polynomials in the non-commutative variables $x_1, x_2, \ldots, x_n$ with ...
Anouk Bergeron-Brlek +2 more
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Kronecker coefficients: the tensor square conjecture and unimodality [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We consider two aspects of Kronecker coefficients in the directions of representation theory and combinatorics. We consider a conjecture of Jan Saxl stating that the tensor square of the $S_n$-irreducible representation indexed by the staircase partition
Igor Pak, Greta Panova, Ernesto Vallejo
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Products of symmetric group characters
Journal of Combinatorial Theory, 2019 In [33] , the authors introduced a new basis of the ring of symmetric functions which evaluate to the irreducible characters of the symmetric group at roots of unity. The structure coefficients for this new basis are the stable Kronecker coefficients. In
R. Orellana, M. Zabrocki
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Symmetric groups and expanders [PDF]
Electronic Research Announcements of the American Mathematical Society, 2005 We construct explicit generating sets F n F_n and F ~ n \tilde F_n of the alternating and the symmetric groups, which turn the Cayley graphs C ( A l t (
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Word Measures on Symmetric Groups
International Mathematics Research Notices, 2022 AbstractFix a word $ w $ in a free group $ \textbf {F}$ on $r$ generators. A $w$-random permutation in the symmetric group $S_{N}$ is obtained by sampling $r$ independent uniformly random permutations $ \sigma _{1},\ldots ,\sigma _{r}\in S_{N}$ and evaluating $w\left (\sigma _{1},\ldots ,\sigma _{r}\right )$.
Hanany, Liam, Puder, Doron
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Invariable generation of the symmetric group [PDF]
, 2015 We say that permutations $\pi_1,\dots, \pi_r \in \mathcal{S}_n$ invariably generate $\mathcal{S}_n$ if, no matter how one chooses conjugates $\pi'_1,\dots,\pi'_r$ of these permutations, $\pi'_1,\dots,\pi'_r$ generate $\mathcal{S}_n$.
Sean Eberhard, Kevin Ford, B. Green
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Symmetries among Multivariate Information Measures Explored Using Möbius Operators
Entropy, 2019 Relations between common information measures include the duality relations based on Möbius inversion on lattices, which are the direct consequence of the symmetries of the lattices of the sets of variables (subsets ordered by inclusion).
David J. Galas, Nikita A. Sakhanenko
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QUANTUM ISOMETRY GROUPS OF SYMMETRIC GROUPS [PDF]
International Journal of Mathematics, 2012 We identify the quantum isometry groups of spectral triples built on the symmetric groups with length functions arising from the nearest-neighbor transpositions as generators. It turns out that they are isomorphic to certain "doubling" of the group algebras of the respective symmetric groups.
Liszka-Dalecki, Jan, Sołtan, Piotr M.
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Cayley graph on symmetric group generated by elements fixing k points [PDF]
, 2014 Let S n be the symmetric group on [ n ] = { 1 , … , n } . The k-point fixing graph F ( n , k ) is defined to be the graph with vertex set S n and two vertices g, h of F ( n , k ) are joined if and only if g h − 1 fixes exactly k points. In this paper, we
Kok Bin Wong, T. Lau, C. Y. Ku
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