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The Sorting Index and Permutation Codes
Permutation statistics Mahonian statistics Coxeter groups Set-valued statistics Bijections
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2012/6/19
In the combinatorial study of the coefficients of a bivariate polynomial that generalizes both the length and the reflection length generating functions for finite Coxeter groups, Petersen introduced ...
Expected Patterns in Permutation Classes
Expected Patterns Permutation Classes Combinatorics
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2012/6/15
In the set of all patterns in $S_n$, it is clear that each k-pattern occurs equally often. If we instead restrict to the class of permutations avoiding a specific pattern, the situation quickly become...
Combinatorial specification of permutation classes
permutation classes excluded patterns substitution decomposition simple permutations generating functions combinatorial specification random generation
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2012/4/23
This article presents a methodology that automatically derives a combinatorial specification for the permutation class C = Av(B), given its basis B of excluded patterns and the set of simple permutati...
Quasi-Permutation Representations of Groups of Order 64
Quasi-permutation representations 2-groups Character theory
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2010/2/25
In [1], we gave algorithms to calculate c(G), q(G) and p(G) for a finite group G. In this paper, we will calculate c(G), q(G), p(G) for non-abelian groups G, where |G|=64.