Cyclic sieving and cluster multicomplexes

Details Cyclic sieving and cluster multicomplexes Cyclic sieving and cluster multicomplexes

2010-05-14

arxiv.org/abs/1005.2561v1

Mathematics

Combinatorics

To appear in Adv. Appl. Math

Scientific paper

Reiner, Stanton, and White \cite{RSWCSP} proved results regarding the enumeration of polygon dissections up to rotational symmetry. Eu and Fu \cite{EuFu} 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 \cite{FZY}. 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 semi-noncrossing tableaux due to Pylyavskyy \cite{PN} as well as some geometric realizations of finite type cluster algebras due to Fomin and Zelevinsky \cite{FZClusterII}.

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