Rational Dyck Paths in the Non Relatively Prime Case

Eugene Gorsky (1) , Mikhail Mazin (2) , Monica Vazirani (1)

1 UC Davis - University of California [Davis]
2 Department of Mathematics [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.

Domaines: Combinatoire [math.CO]

Eugene Gorsky, Mikhail Mazin, Monica Vazirani. Rational Dyck Paths in the Non Relatively Prime Case. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6387⟩. ⟨hal-02168297⟩