Results 51 to 60 of about 15,374,978 (303)
On the Modular Representations of the Symmetric Group (III) [PDF]
Proceedings of the National Academy of Sciences, 1951 1. Introduction. It has been observed (2) that the number of p-regular classes of Sn, i.e. the number of classes of order prime to p, is equal to the number of partitions (λ) of n in which no summand is repeated p or more times. For this relation to hold it is essential that p be prime. It seems natural to call the Young diagram [λ] associated with (λ)
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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 symmetric genus of alternating and symmetric groups
Journal of Combinatorial Theory, Series B, 1985 The symmetric genus of a finite group G has been defined by Thomas W. Tucker as the smallest genus of all surfaces on which G acts faithfully as a group of automorphisms (some of which may reverse the orientation of the surface). This note announces the symmetric genus of all finite alternating and symmetric groups.
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Subgroups of Infinite Symmetric Groups
Journal of the London Mathematical Society, 1990 Various questions are discussed on the subgroup structure of \(S:=Sym(\Omega)\), where \(\Omega\) is an infinite set. It is shown that S is not the union of a chain of size \(| \Omega |\) of proper subgroups, and results are obtained on the size of the smallest families of proper subgroups with set-theoretic union S.
Macpherson, H, Neumann, P
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Background Platinum‐based chemotherapy is known to cause severe and debilitating hearing loss, but unlike cisplatin, the true incidence of carboplatin‐induced hearing loss remains unclear. We evaluated functional hearing outcomes in children receiving carboplatin to determine the incidence and severity of ototoxicity. Procedure We identified a
Aniket Chawla +6 more
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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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Diversity and complexity in neural organoids
FEBS Letters, EarlyView.Neural organoid research aims to expand genetic diversity on one side and increase tissue complexity on the other. Chimeroids integrate multiple donor genomes within single organoids. Self‐organising multi‐identity organoids, exogenous cell seeding, or enforced assembly of region‐specific organoids contribute to tissue complexity.
Ilaria Chiaradia, Madeline A. Lancaster
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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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Symmetric groups and expander graphs [PDF]
Inventiones mathematicae, 2007 We construct explicit generating sets S_n and \tilde S_n of the for the alternating and the symmetric groups, which turn the Cayley graphs C(Alt(n), S_n) and C(Sym(n), \tilde S_n) into a family of bounded degree expanders for all n. This answers affirmatively an old question which has been asked many times in the literature.
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