Séminaire Lotharingien de Combinatoire, 91B.89 (2024), 12 pp.
Olya Mandelshtam and Jerónimo Valencia-Porras
Charge Formulas for Macdonald Polynomials at t = 0 from Multiline Queues and Diagrams
Abstract.
Multiline queues are combinatorial objects coming from probability
theory that give formulas for the q-Whittaker specialization
Pλ(X;q,0) of the Macdonald
polynomials. We define a charge
statistic and an RSK-esque procedure on multiline queues that
naturally recovers the Schur expansion
of Pλ(X;q,0). We
extend these results to generalized multiline queues, which are
in bijection with binary matrices, and obtain a new family of formulas
for Pλ(X;q,0) in terms of these objects.
Multiline diagrams are the plethystic analogs of multiline queues that
were recently found to give a formula for the modified Hall-Littlewood
polynomials H~λ(X;q,0).
We obtain formulas for
the latter through a cocharge statistic and an RSK-esque procedure on
multiline diagrams.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
The following versions are available: