Rational parking functions and LLT polynomials
- Author(s): Gorsky, E
- Mazin, M
- et al.
Published Web Locationhttps://doi.org/10.1016/j.jcta.2016.01.004
© 2016 Elsevier Inc. 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.