2014/07/21 by Jouhet, Frédéric, Philippe Nadeau, Nadeau, Philippe
Mathematics · #05A15 #05E15 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.1407.5575
openalex publication_date 2014/07/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
An element of a Coxeter group W is called fully commutative if any two of its reduced decompositions can be related by a series of transpositions of adjacent commuting generators. In the preprint "Fully commutative elements in finite and affine Coxeter groups" (arXiv:1402.2166), R. Biagioli and the authors proved among other things that, for each irreducible affine Coxeter group, the sequence counting fully commutative elements with respect to length is ultimately periodic. In the present work, we study this sequence in its periodic part for each of these groups, and in particular we determine the minimal period. We also observe that in type A affine we get an instance of the cyclic sieving phenomenon.