Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Rational Dyck Paths in the Non Relatively Prime Case
Eugene Gorsky  1, 2  , Mikhail Mazin  3  , Monica Vazirani  2  
1 : International Laboratory of Representation Theory and Mathematical Physics, NRU-HSE, Moscow
2 : University of California [Davis, USA]  (UC Davis)  -  Website
One Shields Avenue, , Davis, CA 95616-5294 -  États-Unis
3 : Department of Mathematics [Kansas]  -  Website
Department of Mathematics Kansas State University Manhattan -  États-Unis

We study the relationship between rational slope Dyck paths and invariant subsets in Z, extending the work of the first two authors in the relatively prime case. We also find a bijection between (dn, dm)–Dyck paths and d-tuples of (n, m)-Dyck paths endowed with certain gluing data. These are first steps towards understanding the relationship between the rational slope Catalan combinatorics in non relatively prime case and the geometry of affine Springer fibers and representation theory. 

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