Mathematics – Quantum Algebra
Scientific paper
2004-10-04
Mathematics
Quantum Algebra
21 pages, 3 figures
Scientific paper
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.
Chapoton Frederic
Vallette Bruno
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