Bruhat order on plane posets and applications - Archive ouverte HAL Access content directly
Journal Articles J. Comb. Theory, Ser. A Year : 2014

Bruhat order on plane posets and applications

Loïc Foissy


A plane poset is a finite set with two partial orders, satisfying a certain incompatibility condition. The set PP of isoclasses of plane posets owns two products, and an infinitesimal Hopf algebra structure is defined on the vector space H_PP generated by PP, using the notion of biideals of plane posets. We here define a partial order on PP, making it isomorphic to the set of partitions with the weak Bruhat order. We prove that this order is compatible with both products of PP; moreover, it encodes a non degenerate Hopf pairing on the infinitesimal Hopf algebra H_PP.
Fichier principal
Vignette du fichier
doubleposets.pdf (210.37 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00756436 , version 1 (23-11-2012)



Loïc Foissy. Bruhat order on plane posets and applications. J. Comb. Theory, Ser. A, 2014. ⟨hal-00756436⟩
58 View
124 Download



Gmail Facebook X LinkedIn More