15 citations · 65 across the 16 of their papers we have counts for
5 papers · 1 filter
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: 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…
Grid classes and the Fibonacci dichotomy for restricted permutations
Sophie Huczynska, Vincent Vatter
We introduce and characterise grid classes, which are natural generalisations of other well-studied permutation classes. This characterisation allows us to give a new, short proof…