2004/10/04 by Frederic Chapoton, Frédéric Chapoton, Chapoton, Frederic +2 · 1 citation
Mathematics · #06A11 Secondary 18D50 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #MSC2000 : Primary 05E25 #Quantum Algebra (math.QA) #math.QA #msc:05E25 #msc:06A11 #msc:18D50 #msc:MSC2000
paper · pdf · doi:10.48550/arxiv.math/0410051
21 pages, 3 figures
arxiv created 2004/10/04 · openalex publication_date 2004/10/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to define and study pointed and multi-pointed partition posets of type A and B (in the classification of Coxeter groups). We compute their characteristic polynomials, incidence Hopf algebras and homology groups. As a corollary, we get that some operads are Koszul over Z. Cet article introduit et etudie les posets des partitions pointees et multi-pointees en type A et B (dans la classification des groupes de Coxeter finis). Leurs polynomes caracteristiques, leurs algebres de Hopf d'incidence et leurs groupes d'homologie sont calcules. Comme corollaire, on obtient que certaines operades sont de Koszul sur Z.