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The Sorting Index and Permutation Codes
Permutation statistics Mahonian statistics Coxeter groups Set-valued statistics Bijections
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
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
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
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.