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The cohomology of the symmetric groups [PDF]
Transactions of the American Mathematical Society, 1978 Let S n {{\mathcal {S}}_n} be the symmetric group on n letters and SG the limit of the sets of degree +1 homotopy equivalences of the n − 1 n - 1 sphere. Let p be an odd prime.
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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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On the separation of eigenvalues by the permutation group
Special Matrices, 2014 Let A be an invertible 3 × 3 complex matrix. It is shown that there is a 3 × 3 permutation matrix P such that the product PA has at least two distinct eigenvalues.
Cigler Grega, Jerman Marjan
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On symmetric units in group algebras
, 2000 Let $U(KG)$ be the group of units of the group ring $KG$ of the group $G$ over a commutative ring $K$. The anti-automorphism $g\mapsto g\m1$ of $G$ can be extended linearly to an anti-automorphism $a\mapsto a^*$ of $KG$. Let $S_*(KG)=\{x\in U(KG) \mid x^*
Bovdi, Victor
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Branching rules in the ring of superclass functions of unipotent upper-triangular matrices [PDF]
, 2008 It is becoming increasingly clear that the supercharacter theory of the finite group of unipotent upper-triangular matrices has a rich combinatorial structure built on set-partitions that is analogous to the partition combinatorics of the classical ...
Thiem, Nathaniel
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On double cosets with the trivial intersection property and Kazhdan-Lusztig cells in S n [PDF]
International Journal of Group Theory, 2015 For a composition λ of n our aim is to obtain reduced forms for all the elements in the Kazhdan-Lusztig (right) cell containing w J(λ) , the longest element of the standard parabolic subgroup of S n corresponding to λ .
Thomas P. McDonough +1 more
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Symmetric differentials and the fundamental group
, 2013 Esnault asked whether every smooth complex projective variety with infinite fundamental group has a nonzero symmetric differential (a section of a symmetric power of the cotangent bundle).
Brunebarbe, Yohan +2 more
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The Sylow subgroups of the symmetric groups [PDF]
Proceedings of the American Mathematical Society, 1955 particular representation by means of "reduced polynomials."' It has seemed worth while to restate some of his results using the concept of complete product L o M of two permutation groups L, M which he and Krasner have recently emphasised.2 This elementary notion is of great importance in the theory of finite groups and it appears in the literature in
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