Rational Parking Functions and LLT Polynomials
Combinatorics
2016-03-15 v1 Representation Theory
Abstract
We prove that the combinatorial side of the "Rational Shuffle Conjecture" provides a Schur-positive symmetric polynomial. Furthermore, we prove that the contribution of a given rational Dyck path can be computed as a certain skew LLT polynomial, thus generalizing the result of Haglund, Haiman, Loehr, Remmel and Ulyanov. The corresponding skew diagram is described explicitly in terms of a certain (m,n)-core.
Cite
@article{arxiv.1503.04181,
title = {Rational Parking Functions and LLT Polynomials},
author = {Eugene Gorsky and Mikhail Mazin},
journal= {arXiv preprint arXiv:1503.04181},
year = {2016}
}
Comments
14 pages, 8 figures