Journal of Homotopy and Related Structures

, Volume 10, Issue 2, pp 205–238 | Cite as

Bipermutahedron and biassociahedron

  • Martin Markl


We give a simple description of the face poset of a version of the biassociahedra that generalizes, in a straightforward manner, the description of the faces of the Stasheff’s associahedra via planar trees. We believe that our description will substantially simplify the notation of Saneblidze and Umble (Homology Homotopy Appl 13(1):1–57, 2011) making it, as well as the related papers, more accessible.


Permutahedron Associahedron Tree Operad PROP Zone Diaphragm 

Mathematics Subject Classification (2000)

16W30 57T05 18C10 18G99 



I would like to express my gratitude to Samson Saneblidze, Jim Stasheff, Ron Umble and the anonymous referee for reading the manuscript and offering helpful remarks and suggestions. I also enjoyed the wonderful atmosphere in the Max-Planck Institut für Matematik in Bonn during the period when the first draft of this paper was completed.


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Copyright information

© Tbilisi Centre for Mathematical Sciences 2013

Authors and Affiliations

  1. 1.Institute of MathematicsCzech AcademyPragueThe Czech Republic
  2. 2.MFF UKPragueThe Czech Republic

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