Length enumeration of fully commutative elements in finite and affine Coxeter groups
| Autor: | Frédéric Jouhet, Philippe Nadeau, Riccardo Biagioli, Mireille Bousquet-Mélou |
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| Přispěvatelé: | Combinatoire, théorie des nombres (CTN), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Centre National de la Recherche Scientifique (CNRS), Biagioli R, Bousquet-Melou M, Jouhet F, Nadeau P |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Sequence
Pure mathematics Algebra and Number Theory 010102 general mathematics Coxeter group 0102 computer and information sciences 01 natural sciences Expression (mathematics) fully commutative elements Coxeter groups 010201 computation theory & mathematics [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] Enumeration FOS: Mathematics Mathematics - Combinatorics Affine transformation Combinatorics (math.CO) 0101 mathematics Element (category theory) Focus (optics) Commutative property Mathematics |
| Zdroj: | Journal of Algebra Journal of Algebra, Elsevier, 2018, 513, pp.466-515. ⟨10.1016/j.jalgebra.2018.06.009⟩ |
| ISSN: | 0021-8693 1090-266X |
| DOI: | 10.1016/j.jalgebra.2018.06.009⟩ |
| Popis: | An element w of a Coxeter group W is said to be fully commutative, if any reduced expression of w can be obtained from any other by transposing adjacent pairs of generators. These elements were described in 1996 by Stembridge in the case of finite irreducible groups, and more recently by Biagioli, Jouhet and Nadeau (BJN) in the affine cases. We focus here on the length enumeration of these elements. Using a recursive description, BJN established for the associated generating functions systems of non-linear q-equations. Here, we show that an alternative recursive description leads to explicit expressions for these generating functions. Comment: 37 pages, 7 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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