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Regular version of the site

Article

Rational Parking Functions and LLT Polynomials

Journal of Combinatorial Theory, Series A. 2016. Vol. 140. P. 123-140.
Gorsky E., Mazin M.

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.