Compactified Jacobians and q,t-Catalan numbers, II

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• 作者：Evgeny Gorsky (1)
  Mikhail Mazin (2)
  
• 关键词：q ; t ; Catalan numbers ; Compactified Jacobian ; Semigroup
• 刊名：Journal of Algebraic Combinatorics
• 出版年：2014
• 出版时间：February 2014
• 年：2014
• 卷：39
• 期：1
• 页码：153-186
• 全文大小：
• 作者单位：Evgeny Gorsky (1)
  Mikhail Mazin (2)
  
  1. Mathematics Department, Stony Brook University, Stony Brook, NY, 11794, USA
  2. Institute for Mathematical Sciences, Stony Brook University, Stony Brook, NY, 11794, USA
  
• ISSN：1572-9192

文摘

We continue the study of the rational-slope generalized q,t-Catalan numbers c m,n (q,t). We describe generalizations of the bijective constructions of J.Haglund and N.Loehr and use them to prove a weak symmetry property c m,n (q,1)=c m,n (1,q) for m=kn. We give a bijective proof of the full symmetry c m,n (q,t)=c m,n (t,q) for min(m,n). As a corollary of these combinatorial constructions, we give a simple formula for the Poincarpolynomials of compactified Jacobians of plane curve singularities x kn=y n . We also give a geometric interpretation of a relation between rational-slope Catalan numbers and the theory of (m,n)-cores discovered by J.Anderson.