Cyclic sieving and cluster multicomplexes

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Abstract

Reiner, Stanton and White (2004) [10] proved results regarding the enumeration of polygon dissections up to rotational symmetry. Eu and Fu (2008) [2] generalized these results to Cartan-Killing types other than A by means of actions of deformed Coxeter elements on cluster complexes of Fomin and Zelevinsky (2003) [6]. The Reiner-Stanton-White and Eu-Fu results were proven using direct counting arguments. We give representation theoretic proofs of closely related results using the notion of noncrossing and seminoncrossing tableaux due to Pylyavskyy (2009) [9] as well as some geometric realizations of finite type cluster algebras due to Fomin and Zelevinsky (2003) [5]. © 2010 Elsevier Inc. All rights reserved.

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Rhoades, B. (2010). Cyclic sieving and cluster multicomplexes. Advances in Applied Mathematics, 45(4), 470–486. https://doi.org/10.1016/j.aam.2010.03.003

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