Results 11 to 20 of about 2,040 (216)
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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Minimal Factorizations of Permutations into Star Transpositions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We give a compact expression for the number of factorizations of any permutation into a minimal number of transpositions of the form $(1 i)$. Our result generalizes earlier work of Pak ($\textit{Reduced decompositions of permutations in terms of star ...
J. Irving, A. Rattan
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The Bruhat order on conjugation-invariant sets of involutions in the symmetric group [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 12 pages, 3 ...
Mikael Hansson
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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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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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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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Harmonic Bernoulli strings and random permutations
Lietuvos Matematikos Rinkinys, 2004 We examine fairly special b-harmonic Bernoulli strings appearing in n observations. It is shown that their count number can be used to define a random process converging to the Brownian motion as n tends to infinity.
Eugenius Manstavičius
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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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Statistical physics of the symmetric group [PDF]
Physical Review E, 2017 12 pages, 4 figures, 1 ...
Williams, Mobolaji, Shakhnovich, Eugene
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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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