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Polytopal Realizations of Generalized Associahedra

Published online by Cambridge University Press:  20 November 2018

Frédéric Chapoton ,
Sergey Fomin  and
Andrei Zelevinsky
Frédéric Chapoton
Affiliation:
LACIM Université du Québec à Montréal Montréal, Québec H3C 3P8, e-mail: chapoton@lacim.uqam.ca
Sergey Fomin
Affiliation:
Department of Mathematics University of Michigan Ann Arbor, Michigan 48109 U.S.A., e-mail: fomin@umich.edu
Andrei Zelevinsky
Affiliation:
Department of Mathematics Northeastern University Boston, Massachusetts 02115 U.S.A., e-mail: andrei@neu.edu
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Abstract

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We prove polytopality of the generalized associahedra introduced in [5].

Keywords

05E1520F5552C07
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 4 , 01 December 2002 , pp. 537 - 566
Copyright
Copyright © Canadian Mathematical Society 2002

References

[1] Bott, R. and Taubes, C., On the self-linking of knots. Topology and physics. J. Math. Phys. (10) 35 (1994), 5247–5287.Google Scholar
[2] Bourbaki, N., Groupes et algèbres de Lie. Chapters IV-VI, Hermann, Paris, 1968.Google Scholar
[3] Devadoss, S. L., A space of cyclohedra. Electronic preprint math. QA/0102166.Google Scholar
[4] Fomin, S. and Zelevinsky, A., Cluster algebras I: Foundations. J. Amer. Math. Soc., to appear.Google Scholar
[5] Fomin, S. and Zelevinsky, A., Y-systems and generalized associahedra. Electronic preprint hep-th/0111053, November, 2001.Google Scholar
[6] Gelfand, I., Kapranov, M., and Zelevinsky, A., Discriminants, Resultants and Multidimensional Determinants. Birkhäuser Boston, 1994.Google Scholar
[7] Kac, V., Infinite dimensional Lie algebras. 3rd edition, Cambridge University Press, 1990.Google Scholar
[8] Lee, C. W., The associahedron and triangulations of the n-gon. European J. Combin. (6) 10 (1989), 551–560.Google Scholar
[9] Markl, M., Simplex, associahedron, and cyclohedron. Contemp.Math. 227 (1999), 235–265.Google Scholar
[10] Reiner, V., Non-crossing partitions for classical reflection groups. Discrete Math. 177 (1997), 195–222.Google Scholar
[11] Simion, R., Noncrossing partitions. Discrete Math. (1–3) 217 (2000), 367–409.Google Scholar
[12] Simion, R., A type-B associahedron. Adv. in Appl. Math., to appear.Google Scholar
[13] Stasheff, J. D., Homotopy associativity of H-spaces. I, II. Trans. Amer.Math. Soc. 108 (1963), 275–292, 293–312.Google Scholar
[14] Stasheff, J. D., From operads to .physically. inspired theories. Contemp.Math. 202 (1997), 53–81.Google Scholar
[15] Ziegler, G. M., Lectures on polytopes. Springer-Verlag, New York, 1995.Google Scholar