Cyclic sieving and cluster multicomplexes

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• 作者：Brendon Rhoades
• 关键词：Fixed point enumeration ; Simplicial complex ; Finite type cluster algebra ; Polygon dissection
• 刊名：Advances in Applied Mathematics
• 出版年：2010
• 出版时间：October 2010
• 年：2010
• 卷：45
• 期：4
• 页码：470-486
• 全文大小：275 K

文摘

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].