Séminaire Lotharingien de Combinatoire, 84B.34 (2020), 12 pp.
Sylvie Corteel, Jim Haglund, Olya Mandelshtam, Sarah Mason and Lauren Williams
Compact Formulas for Macdonald Polynomials and Quasisymmetric Macdonald Polynomials
Abstract.
We present several new and compact formulas for the modified and integral form of the Macdonald polynomials, building on the
compact "multiline queue" formula for Macdonald polynomials
due to Corteel, Mandelshtam and Williams.
We also introduce
a new quasisymmetric analogue of Macdonald polynomials. These
quasisymmetric Macdonald polynomials refine
the (symmetric) Macdonald polynomials and specialize
at $q=t=0$ to the quasisymmetric Schur polynomials defined by Haglund, Luoto, Mason, and Van Willigenburg.
Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.
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