2015/11/27 by Philippe Nadeau, Nadeau, Philippe
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA) #math.CO #math.RA #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1511.08788
19 pages
arxiv created 2015/11/27 · openalex publication_date 2015/11/27 · arxiv updated 2015/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a Coxeter group W, an element is fully commutative if any two of its reduced expressions can be linked by a series of commutation of adjacent letters. These elements have particularly nice combinatorial properties, and also index a basis of the generalized Temperley--Lieb algebra attached to W. We give two results about the sequence counting these elements with respect to their Coxeter length. First we prove that it always satisfies a linear recurrence with constant coefficients, by showing that reduced expressions of fully commutative elements form a regular language. Then we classify those groups W for which the sequence is ultimately periodic, extending a result of Stembridge. These results are applied to the growth of generalized Temperley--Lieb algebras.