Skip to main content Accessibility help
×
Home
Hostname: page-component-544b6db54f-bkjnw Total loading time: 0.19 Render date: 2021-10-21T06:30:59.642Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Polytopal Realizations of Generalized Associahedra

Published online by Cambridge University Press:  20 November 2018

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
Rights & Permissions[Opens in a new window]

Abstract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Keywords

Type
Research Article
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), 52475287.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.CrossRefGoogle Scholar
[7] Kac, V., Infinite dimensional Lie algebras. 3rd edition, Cambridge University Press, 1990.CrossRefGoogle Scholar
[8] Lee, C. W., The associahedron and triangulations of the n-gon. European J. Combin. (6) 10 (1989), 551560.Google Scholar
[9] Markl, M., Simplex, associahedron, and cyclohedron. Contemp.Math. 227 (1999), 235265.Google Scholar
[10] Reiner, V., Non-crossing partitions for classical reflection groups. Discrete Math. 177 (1997), 195222.Google Scholar
[11] Simion, R., Noncrossing partitions. Discrete Math. (13) 217 (2000), 367409.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), 275292, 293312.Google Scholar
[14] Stasheff, J. D., From operads to .physically. inspired theories. Contemp.Math. 202 (1997), 5381.Google Scholar
[15] Ziegler, G. M., Lectures on polytopes. Springer-Verlag, New York, 1995.CrossRefGoogle Scholar
You have Access
57
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Polytopal Realizations of Generalized Associahedra
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Polytopal Realizations of Generalized Associahedra
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Polytopal Realizations of Generalized Associahedra
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *