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.6387
Rational Dyck Paths in the Non Relatively Prime Case

Authors: Eugene Gorsky ORCID-iD1; 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.

https://doi.org/10.46298/dmtcs.6387
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

Linked publications - datasets - softwares

Source : ScholeXplorer IsRelatedTo ARXIV alg-geom/9701019
Source : ScholeXplorer IsRelatedTo DOI 10.1215/s0012-7094-99-09704-1
Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.alg-geom/9701019
  • alg-geom/9701019
  • 10.1215/s0012-7094-99-09704-1
  • 10.1215/s0012-7094-99-09704-1
  • 10.48550/arxiv.alg-geom/9701019
COUNTING RATIONAL CURVES ON K3 SURFACES

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