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Journal Articles Journal of Algebra Year : 2015

The Hopf algebra of finite topologies and T-partitions

Abstract

A noncommutative and noncocommutative Hopf algebra on finite topologies H_T 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 H_T 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.
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Dates and versions

hal-01017229 , version 1 (02-07-2014)
hal-01017229 , version 2 (03-10-2014)

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Cite

Loïc Foissy, Claudia Malvenuto. The Hopf algebra of finite topologies and T-partitions. Journal of Algebra, 2015. ⟨hal-01017229v2⟩
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