Une opérade anticyclique sur les arbustes

Frédéric Chapoton[1]

  • [1] Université de Lyon ; Université Lyon 1 ; CNRS, UMR5208, Institut Camille Jordan, 43 blvd du 11 novembre 1918, F-69622 Villeurbanne-Cedex, France

Annales mathématiques Blaise Pascal (2010)

  • Volume: 17, Issue: 1, page 17-45
  • ISSN: 1259-1734

Abstract

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We define new combinatorial objects, called shrubs, such that forests of rooted trees are shrubs. We then introduce a structure of operad on shrubs. We show that this operad is contained in the Zinbiel operad, by using the inclusion of Zinbiel in the operad of moulds. We also prove that this inclusion is compatible with the richer structure of anticyclic operad that exists on Zinbiel and on moulds.

How to cite

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Chapoton, Frédéric. "Une opérade anticyclique sur les arbustes." Annales mathématiques Blaise Pascal 17.1 (2010): 17-45. <http://eudml.org/doc/116347>.

@article{Chapoton2010,
abstract = {We define new combinatorial objects, called shrubs, such that forests of rooted trees are shrubs. We then introduce a structure of operad on shrubs. We show that this operad is contained in the Zinbiel operad, by using the inclusion of Zinbiel in the operad of moulds. We also prove that this inclusion is compatible with the richer structure of anticyclic operad that exists on Zinbiel and on moulds.},
affiliation = {Université de Lyon ; Université Lyon 1 ; CNRS, UMR5208, Institut Camille Jordan, 43 blvd du 11 novembre 1918, F-69622 Villeurbanne-Cedex, France},
author = {Chapoton, Frédéric},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Operad; anticyclic operad; tree; permutation; fraction},
language = {fre},
month = {1},
number = {1},
pages = {17-45},
publisher = {Annales mathématiques Blaise Pascal},
title = {Une opérade anticyclique sur les arbustes},
url = {http://eudml.org/doc/116347},
volume = {17},
year = {2010},
}

TY - JOUR
AU - Chapoton, Frédéric
TI - Une opérade anticyclique sur les arbustes
JO - Annales mathématiques Blaise Pascal
DA - 2010/1//
PB - Annales mathématiques Blaise Pascal
VL - 17
IS - 1
SP - 17
EP - 45
AB - We define new combinatorial objects, called shrubs, such that forests of rooted trees are shrubs. We then introduce a structure of operad on shrubs. We show that this operad is contained in the Zinbiel operad, by using the inclusion of Zinbiel in the operad of moulds. We also prove that this inclusion is compatible with the richer structure of anticyclic operad that exists on Zinbiel and on moulds.
LA - fre
KW - Operad; anticyclic operad; tree; permutation; fraction
UR - http://eudml.org/doc/116347
ER -

References

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  1. F. Bergeron, G. Labelle, P. Leroux, Combinatorial species and tree-like structures, 67 (1998), Cambridge University Press, Cambridge Zbl0888.05001MR1629341
  2. F. Chapoton, On some anticyclic operads, Algebr. Geom. Topol. 5 (2005), 53-69 (electronic) Zbl1060.18004MR2135545
  3. F. Chapoton, The anticyclic operad of moulds, Int. Math. Res. Not. IMRN (2007) Zbl1149.18004MR2363304
  4. Frédéric Chapoton, A bijection between shrubs and series-parallel posets, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008) 
  5. Frédéric Chapoton, Florent Hivert, Jean-Christophe Novelli, Jean-Yves Thibon, An operational calculus for the mould operad, Int. Math. Res. Not. IMRN (2008) Zbl1146.18301MR2429249
  6. Muriel Livernet, A rigidity theorem for pre-Lie algebras, J. Pure Appl. Algebra 207 (2006), 1-18 Zbl1134.17001MR2244257
  7. Jean-Louis Loday, Dialgebras, Dialgebras and related operads 1763 (2001), 7-66, Springer, Berlin Zbl0999.17002MR1860994
  8. Jean-Louis Loday, Maria O. Ronco, Combinatorial Hopf algebras, (2008) Zbl1217.16033
  9. Richard P. Stanley, Enumeration of posets generated by disjoint unions and ordinal sums, Proc. Amer. Math. Soc. 45 (1974), 295-299 Zbl0297.05009MR351928
  10. Richard P. Stanley, Enumerative combinatorics. Vol. 2, 62 (1999), Cambridge University Press, Cambridge Zbl0928.05001MR1676282

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