The dendriform module on the cyclic group

Frédéric Chapoton[1]

  • [1] Université Claude Bernard Lyon 1 Institut Camille Jordan 21 avenue Claude Bernard 69622 Villeurbanne cedex (France)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 7, page 2333-2350
  • ISSN: 0373-0956

Abstract

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It is known that the Dendriform operad is in fact an anticyclic operad. This refined structure defines in particular a matrix of finite order acting on the vector space spanned by planar binary trees. We compute here its characteristic polynomial and propose a compatible conjecture for the characteristic polynomial of the Coxeter transformation for the Tamari lattice, which is essentially a square root of this matrix.

How to cite

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Chapoton, Frédéric. "Le module dendriforme sur le groupe cyclique." Annales de l’institut Fourier 58.7 (2008): 2333-2350. <http://eudml.org/doc/10380>.

@article{Chapoton2008,
abstract = {La structure d’opérade anticyclique de l’opérade dendriforme donne en particulier une matrice d’ordre $n$ agissant sur l’espace engendré par les arbres binaires plans à $n$ feuilles. On calcule le polynôme caractéristique de cette matrice. On propose aussi une conjecture compatible pour le polynôme caractéristique de la transformation de Coxeter du poset de Tamari, qui est essentiellement une racine carrée de cette matrice.},
affiliation = {Université Claude Bernard Lyon 1 Institut Camille Jordan 21 avenue Claude Bernard 69622 Villeurbanne cedex (France)},
author = {Chapoton, Frédéric},
journal = {Annales de l’institut Fourier},
keywords = {Dendriform operad; anticyclic operad; Tamari lattice; Coxeter transformation},
language = {fre},
number = {7},
pages = {2333-2350},
publisher = {Association des Annales de l’institut Fourier},
title = {Le module dendriforme sur le groupe cyclique},
url = {http://eudml.org/doc/10380},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Chapoton, Frédéric
TI - Le module dendriforme sur le groupe cyclique
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 7
SP - 2333
EP - 2350
AB - La structure d’opérade anticyclique de l’opérade dendriforme donne en particulier une matrice d’ordre $n$ agissant sur l’espace engendré par les arbres binaires plans à $n$ feuilles. On calcule le polynôme caractéristique de cette matrice. On propose aussi une conjecture compatible pour le polynôme caractéristique de la transformation de Coxeter du poset de Tamari, qui est essentiellement une racine carrée de cette matrice.
LA - fre
KW - Dendriform operad; anticyclic operad; Tamari lattice; Coxeter transformation
UR - http://eudml.org/doc/10380
ER -

References

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