The Weak Order on Pattern-Avoiding Permutations

Brian Drake

Abstract


The weak order on the symmetric group is a well-known partial order which is also a lattice. We consider subposets of the weak order consisting of permutations avoiding a single pattern, characterizing the patterns for which the subposet is a lattice. These patterns have only a single small ascent or descent. We prove that all patterns for which the subposet is a sublattice have length at most three.

Keywords


Weak order; Permutation pattern; Lattice

Full Text: PDF