Rational Dyck Paths in the Non Relatively Prime Case
1 : International Laboratory of Representation Theory and Mathematical Physics, NRU-HSE, Moscow
2 : University of California [Davis, USA]
(UC Davis)
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One Shields Avenue, , Davis, CA 95616-5294 -
États-Unis
3 : Department of Mathematics [Kansas]
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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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