Plane posets, special posets, and permutations - Archive ouverte HAL Access content directly
Journal Articles Advances in Mathematics Year : 2013

Plane posets, special posets, and permutations

Loïc Foissy

Abstract

We study the self-dual Hopf algebra $\h_{\SP}$ of special posets introduced by Malvenuto and Reutenauer and the Hopf algebra morphism from $\h_{\SP}$ to to the Hopf algebra of free quasi-symmetric functions $\FQSym$ given by linear extensions. In particular, we construct two Hopf subalgebras both isomorphic to $\FQSym$; the first one is based on plane posets, the second one on heap-ordered forests. An explicit isomorphism between these two Hopf subalgebras is also defined with the help of two transformations on special posets. The restriction of the Hopf pairing of $\h_{\SP}$ to these Hopf subalgebras and others is also studied, as well as certain isometries between them. These problems are solved using duplicial and dendriform structures. An error in Section 7 has been noticed by Darij Grinberg, and the text has been modified accordingly.
Fichier principal
Vignette du fichier
doubleposet3_v2.pdf (524.22 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00619299 , version 1 (06-09-2011)
hal-00619299 , version 2 (13-04-2012)
hal-00619299 , version 3 (05-04-2013)
hal-00619299 , version 4 (19-06-2020)

Identifiers

Cite

Loïc Foissy. Plane posets, special posets, and permutations. Advances in Mathematics, 2013. ⟨hal-00619299v4⟩

Collections

CNRS URCA LMR
372 View
143 Download

Altmetric

Share

Gmail Facebook X LinkedIn More