Séminaire Lotharingien de Combinatoire, 82B.77 (2019), 12 pp.

Sami Assaf and Stephanie van Willigenburg

Skew key polynomials and the key poset

Abstract. We generalize Young's lattice on integer partitions to a new partial order on weak compositions called the key poset. Saturated chains in this poset correspond to standard key tableaux, the combinatorial objects that generate the key polynomial basis for the polynomial ring, a generalization of the Schur basis for symmetric functions. Generalizing skew Schur functions, we define skew key polynomials in terms of the poset, and, using weak dual equivalence, we give a nonnegative composition Littlewood-Richardson rule for the key expansion of skew key polynomials.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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