Rational Dyck Paths in the Non Relatively Prime Case

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 s...

Full description

Saved in:

Bibliographic Details
Published in:	Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings, 28th...
Main Authors:	Gorsky, Eugene, Mazin, Mikhail, Vazirani, Monica
Format:	Journal Article Conference Proceeding
Language:	English
Published:	DMTCS 22.04.2020 Discrete Mathematics & Theoretical Computer Science
Subjects:	[math.math-co]mathematics [math]/combinatorics [math.co] Combinatorics Mathematics
ISSN:	1365-8050, 1462-7264, 1365-8050
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	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.
ISSN:	1365-8050 1462-7264 1365-8050
DOI:	10.46298/dmtcs.6387