Séminaire Lotharingien de Combinatoire, 80B.77 (2018), 12 pp.
Angela Hicks and Marino Romero
Delta Operators at q=1 and Polyominoes
For a symmetric function G, the Delta operator ΔG is defined
via its action on modified Macdonald polynomials by setting
where Bμ is a
polynomial in q and t. Previous work by Haglund, Remmel, Wilson
conjectures a combinatorial interpretation for Δeken,
generalizing the Shuffle Theorem. Here, we prove combinatorial
expressing each as weighted sum
over (parallelogram) polyominoes in a rectangle, and provide an
explicit combinatorial interpretation for their elementary and Schur
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
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