The enumeration of fully commutative affine permutations

2009/07/03 by Christopher R. H. Hanusa, Hanusa, Christopher R. H., Brant Jones +2
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #math.CO #msc:05A15 #msc:05E15 #msc:20F55

paper · pdf · doi:10.48550/arxiv.0907.0709

18 pages; final version

arxiv created 2009/12/11 · arxiv updated 2010/01/07

Abstract

We give a generating function for the fully commutative affine permutations enumerated by rank and Coxeter length, extending formulas due to Stembridge and Barcucci--Del Lungo--Pergola--Pinzani. For fixed rank, the length generating functions have coefficients that are periodic with period dividing the rank. In the course of proving these formulas, we obtain results that elucidate the structure of the fully commutative affine permutations.

Related

• Long fully commutative elements in affine Coxeter groups
• Fully commutative elements in finite and affine Coxeter groups
• Combinatorics of fully commutative involutions in classical Coxeter groups
• A classification of affine fully commutative elements
• On the length of fully commutative elements