Séminaire Lotharingien de Combinatoire, 89B.84 (2023), 12 pp.
Nicolle González, José Simental and Monica Vazirani
Semistandard Parking Functions and a Finite Shuffle Theorem
Abstract.
We introduce the higher rank rational (q,t)-Catalan
polynomials and prove these are equal to finite truncations of the
Hikita polynomial. We also generalize results of Gorsky-Mazin-Vazirani
and construct an explicit bijection between semistandard parking
functions and affine compositions. Using these results we prove a
finite analogue of the Rational Shuffle Theorem in the context of
spherical double affine Hecke algebras.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
The following versions are available: