Results 11 to 20 of about 1,043,180 (331)
Hypercontractivity on the symmetric group
Forum of Mathematics, SigmaThe hypercontractive inequality is a fundamental result in analysis, with many applications throughout discrete mathematics, theoretical computer science, combinatorics and more.
Yuval Filmus +3 more
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The Characters of the Symmetric Group [PDF]
American Journal of Mathematics, 1937 A short and simple derivation of the formula of Frobenius, which gives the dimensions of the irreducible representations of S n , the symmetric group on any number, n , of symbols, is given.
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Long Cycle Factorizations: Bijective Computation in the General Case [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 This paper is devoted to the computation of the number of ordered factorizations of a long cycle in the symmetric group where the number of factors is arbitrary and the cycle structure of the factors is given. Jackson (1988) derived the first closed form
Ekaterina A. Vassilieva
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Number of terms in the group determinant
Examples and Counterexamples, 2023 In this paper, we prove that when the number of terms in the group determinant of order odd prime p is divided by p, the remainder is 1. In addition, we give a table of the number of terms in kth power of the group determinant of the cyclic group of ...
Naoya Yamaguchi, Yuka Yamaguchi
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The $m$-Cover Posets and the Strip-Decomposition of $m$-Dyck Paths [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 In the first part of this article we present a realization of the $m$-Tamari lattice $\mathcal{T}_n^{(m)}$ in terms of $m$-tuples of Dyck paths of height $n$, equipped with componentwise rotation order. For that, we define the $m$-cover poset $\mathcal{P}
Myrto Kallipoliti, Henri Mühle
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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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On Coprimality Graphs for Symmetric Groups [PDF]
Graphs and Combinatorics, 2012 Let \(G\) be a group, \(X\) be a subset of \(G\) and \(\pi\) be a set of positive integers. We define a graph \(C_\pi(G,X)\) whose vertex set is \(X\) with \(x,y\in X\) joined by an edge provided \(x\neq y\) and the order of \(xy\) is in \(\pi\). Because \(xy\) and \(yx\) are conjugate elements of \(G\), this graph is undirected.
John Ballantyne +2 more
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A preorder-free construction of the Kazhdan-Lusztig representations of $S_n$, with connections to the Clausen representations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We use the polynomial ring $\mathbb{C}[x_{1,1},\ldots,x_{n,n}]$ to modify the Kazhdan-Lusztig construction of irreducible $S_n$-modules. This modified construction produces exactly the same matrices as the original construction in [$\textit{Invent. Math}$
Charles Buehrle, Mark Skandera
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Explicit generating series for connection coefficients [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 This paper is devoted to the explicit computation of generating series for the connection coefficients of two commutative subalgebras of the group algebra of the symmetric group, the class algebra and the double coset algebra. As shown by Hanlon, Stanley
Ekaterina A. Vassilieva
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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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