Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Tuesday 5
Combinatorics
Eric Fusy
› 17:30 - 19:00 (1h30)
› SFU Harbour Center - Segal Centre Conference Rooms 1400 - 1410
Rational Dyck Paths in the Non Relatively Prime Case
Eugene Gorsky  1, 2  , Mikhail Mazin  3  , Monica Vazirani  1  
1 : University of California at Davis, Davis, California
2 : International Laboratory of Representation Theory and Mathematical Physics, NRU-HSE, Moscow
3 : Kansas State University, Manhattan, Kansas

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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