منابع مشابه
Reflection Factorizations of Singer Cycles
The number of shortest factorizations into reflections for a Singer cycle in GLn(Fq) is shown to be (qn − 1)n−1. Formulas counting factorizations of any length, and counting those with reflections of fixed conjugacy classes are also given. The method is a standard character-theory technique, requiring the compilation of irreducible character values for Singer cycles, semisimple reflections, and...
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The main goal of coding theory is to devise efficient systems to exploit the full capacity of a communication channel, thus achieving an arbitrarily small error probability. Low Density Parity Check (LDPC) codes are a family of block codes—characterised by admitting a sparse parity check matrix—with good correction capabilities. In the present paper the orbits of subspaces of a finite projectiv...
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We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings, that is, we study the number Hα(i2, i3, . . . ) of ways a given permutation (with cycles described by the partitionα) can be decomposed into a product of exactly i2 2-cycles, i3 3-cycles, etc., with certain minimality and transitivity conditions imposed on the factors. The method is to ...
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In this paper we present a min-max theorem for a factorization problem in directed graphs. This extends the Berge-Tutte formula on matchings as well as formulas for the maximum even factor in weakly symmetric directed graphs and a factorization problem in undirected graphs. We also prove an extension to the structural theorem of Gallai and Edmonds about a canonical set attaining minimum in the ...
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In [CS12], Chapuy and Stump studied factorizations of Coxeter elements into products of reflections in well-generated, irreducible complex reflection groups, giving a simple closed form expression for their exponential generating function depending on certain natural parameters. In this work, their methods are used to consider a more general multivariate generating function FACW (u1, . . . , u`...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2014
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-014-0502-0