Bipermutahedron and biassociahedron

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• 作者：Martin Markl
• 关键词：Permutahedron ; Associahedron ; Tree ; Operad ; PROP ; Zone ; Diaphragm ; 16W30 ; 57T05 ; 18C10 ; 18G99
• 刊名：Journal of Homotopy and Related Structures
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：10
• 期：2
• 页码：205-238
• 全文大小：1,192 KB
• 参考文献：1.Forcey, S.: Convex hull realizations of the multiplihedra. Topol. Appl. 156(2), 326-47 (2008)View Article MATH MathSciNet
  2.Iwase, N., Mimura, M.: Higher homotopy associativity. In: Algebraic Topology (Arcata, CA, 1986). Lecture Notes in Mathematics, vol. 1370, pp. 193-20. Springer, Berlin (1989)
  3.Jarry, A.: Ubu Roi. Norton anthology of drama, 2010. Translated by David Ball as Ubu the King. The original French version available at http://?www.?gutenberg.?org/?ebooks/-6884
  4.Mac Lane, S.: Natural associativity and commutativity. Rice Univ. Stud. 49(4), 28-6 (1963)MathSciNet
  5.Markl, M.: Models for operads. Commun. Algebra 24(4), 1471-500 (1996)View Article MATH MathSciNet
  6.Markl, M.: Homotopy algebras are homotopy algebras. Forum Math. 16(1), 129-60 (2004)View Article MATH MathSciNet
  7.Markl, M.: A resolution (minimal model) of the PROP for bialgebras. J. Pure Appl. Algebra 205(2), 341-74 (2006)View Article MATH MathSciNet
  8.Markl, M.: Operads and PROPs. In: Handbook of Algebra, vol. 5, pp. 87-40. North-Holland, Amsterdam (2008)
  9.Markl, M., Shnider, S., Stasheff, J.D.: Operads in Algebra, Topology and Physics, volume 96 of Mathematical Surveys and Monographs. American Mathematical Society, Providence (2002)
  10.Saneblidze, S., Umble, R.: Matrads, biassociahedra, and \(A_\infty \) -bialgebras. Homol. Homotopy Appl. 13(1), 1-7 (2011)View Article MATH MathSciNet
  11.Stasheff, J.D.: Homotopy associativity of \(H\) -spaces. I, II. Trans. Am. Math. Soc. 108, 275-12 (1963)
  12.Stasheff, J.D.: H-Spaces from a homotopy point of view. In: Lecture Notes in Math., vol. 161. Springer, New York (1970)
  13.Tamari, D.: The algebra of bracketings and their enumeration. Nieuw Arch. Wisk. (3) 10, 131-46 (1962)
  14.Tonks, A.: Relating the associahedron and the permutohedron. In: Loday, J.L., Stasheff J.D., Voronov, A.A. (eds.) Operads: Proceedings of Renaissance Conferences. Contemporary Mathematics, vol. 202, pp. 33-6. Am. Math. Soc., Providence (1997)
  
• 作者单位：Martin Markl (1) (2)
  
  1. Institute of Mathematics, Czech Academy, ?itná 25, 115?67?, Prague, The Czech Republic
  2. MFF UK, Sokolovská 83, 186?75?, Prague, The Czech Republic
  
• 刊物主题：Algebraic Topology; Algebra; Functional Analysis; Number Theory;
• 出版者：Springer Berlin Heidelberg
• ISSN：1512-2891

文摘

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):1-7, 2011) making it, as well as the related papers, more accessible.