Rational parking functions and LLT polynomials
Copyright policy )Rational parking functions and LLT polynomials
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.
14 pages, 8 figures
- University of California United States
- Kansas State University United States
- National Research University Higher School of Economics Russian Federation
math.RT, simultaneous cores, Computation Theory & Mathematics, shuffle conjecture, 05E05, FOS: Mathematics, Mathematics - Combinatorics, math.CO, Representation Theory (math.RT), Simultaneous cores, 05A17, 05A19, 05A30, 05E05, 05E10, 20C30, Representations of finite symmetric groups, Pure Mathematics, 05A19, LLT polynomials, 05A17, Combinatorial aspects of representation theory, \(q\)-calculus and related topics, Shuffle conjecture, Combinatorics (math.CO), 05A30, 20C30, 05E10, Mathematics - Representation Theory
math.RT, simultaneous cores, Computation Theory & Mathematics, shuffle conjecture, 05E05, FOS: Mathematics, Mathematics - Combinatorics, math.CO, Representation Theory (math.RT), Simultaneous cores, 05A17, 05A19, 05A30, 05E05, 05E10, 20C30, Representations of finite symmetric groups, Pure Mathematics, 05A19, LLT polynomials, 05A17, Combinatorial aspects of representation theory, \(q\)-calculus and related topics, Shuffle conjecture, Combinatorics (math.CO), 05A30, 20C30, 05E10, Mathematics - Representation Theory
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