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Discrete Mathematics & Theoretical Computer Science |
Eugene Gorsky ; Mikhail Mazin ; Monica Vazirani - Rational Dyck Paths in the Non Relatively Prime Case
dmtcs:6387 - Discrete Mathematics & Theoretical Computer Science, April 22, 2020, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) - https://doi.org/10.46298/dmtcs.6387Rational Dyck Paths in the Non Relatively Prime CaseArticle
Authors: Eugene Gorsky 
1; Mikhail Mazin 2; Monica Vazirani 1
- 1 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.
Source: HAL:hal-02168297v1
Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Published on: April 22, 2020
Imported on: July 4, 2016
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
Funding:
- Source : OpenAIRE Graph
- Algebraic Knots and Representation Theory; Funder: National Science Foundation; Code: 1559338
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