14 citations · 78 across the 33 of their papers we have counts for
5 papers · 2 filters
Wreath Products of Permutation Classes
Robert Brignall
A permutation class which is closed under pattern involvement may be described in terms of its basis. The wreath product construction X \wr Y of two permutation classes X and Y is…
Simple permutations: decidability and unavoidable substructures
Robert Brignall, Nik Ruskuc, Vince Vatter
We prove that it is decidable if a finitely based permutation class contains infinitely many simple permutations, and establish an unavoidable substructure result for simple permut…
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…