8 papers
Pattern avoidance in canon permutations
Robert Laudone
A canon permutation is a -regular word over in which, for each , the -th copies of the letters form the same permutation . These were introduced by Elizalde as a…
A lower bound on the growth rate of -avoiding cyclic permutations
Robert Laudone
We construct a new reduction process which takes a -avoiding permutation to a shorter one that is cyclic if and only if the original was. Iterating it determines whether…
Arrow pattern avoidance in permutations: structure and enumeration
Kassie Archer, Robert P. Laudone
Arrow patterns were introduced by Berman and Tenner as a generalization of vincular patterns. They observed that arrow patterns have the potential to bridge the divide between a pe…
Seaweed algebras with restricted part sizes
Kassie Archer, Aaron Geary, Robert P. Laudone
Seaweed algebras are a class of Lie algebras that are naturally characterized by a pair of compositions, which in turn are represented visually as planar graphs called meanders. Th…
Pattern avoidance in non-crossing and non-nesting permutations
Kassie Archer, Robert P. Laudone
Non-crossing and non-nesting permutations are variations of the well-known Stirling permutations. A permutation on is called non-crossing if it avoid…
Characterizing avoidance in cycles via vincular patterns
Robert P. Laudone
We show that cyclic permutations avoiding are precisely those permutations whose image under the fundamental bijection avoid a set of vincular patterns. We do this by using p…