The Hopf algebra of finite topologies and T-partitions

JOURNAL OF ALGEBRA

卷:438

Article

Foissy, Loic¹  Malvenuto, Claudia² 

[1] Univ Littoral Cote dOpale, Ctr Univ Mi Voix, Lab Math Pures & Appl Joseph Liouville, Federat Rech Math Nord Pas de Calais FR 2956, F-62228 Calais, France

[2] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

关键词: Finite topologies;    Combinatorial Hopf algebras;    Packed words;    Partitions;   

DOI  :  10.1016/j.jalgebra.2015.04.024

来源: Elsevier

【 摘 要 】

A noncommutative and noncocommutative Hopf algebra on finite topologies HT is introduced and studied (freeness, cofreeness, self-duality...). Generalizing Stanley's definition of P-partitions associated to a special poset, we define the notion of T-partitions associated to a finite topology, and deduce a Hopf algebra morphism from HT to the Hopf algebra of packed words WQSym. Generalizing Stanley's decomposition by linear extensions, we deduce a factorization of this morphism, which induces a combinatorial isomorphism from the shuffle product to the quasi-shuffle product of WQSym. It is strongly related to a partial order on packed words, here described and studied. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free