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7 papers · 1 filter
The p-modular Descent Algebra of the Symmetric Group
M. D. Atkinson, S. J. van Willigenburg
The descent algebra of the symmetric group, over a field of non-zero characteristic p, is studied. A homomorphism into the algebra of generalised p-modular characters of the symmet…
Reconstructing compositions
Vincent Vatter
We consider the problem of reconstructing compositions of an integer from their subcompositions, which was raised by Raykova (albeit disguised as a question about layered permutati…
Simple permutations and algebraic generating functions
Robert Brignall, Sophie Huczynska, Vincent Vatter
A simple permutation is one that does not map a nontrivial interval onto an interval. It was recently proved by Albert and Atkinson that a permutation class with only finitely simp…
Decomposing simple permutations, with enumerative consequences
Robert Brignall, Sophie Huczynska, Vince Vatter
We prove that every sufficiently long simple permutation contains two long almost disjoint simple subsequences. This result has applications to the enumeration of restricted permut…
Permutation Classes of Polynomial Growth
M. H. Albert, M. D. Atkinson, Robert Brignall
A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of fo…
Enumeration schemes for restricted permutations
Vincent Vatter
Zeilberger's enumeration schemes can be used to completely automate the enumeration of many permutation classes. We extend his enumeration schemes so that they apply to many more p…