Séminaire Lotharingien de Combinatoire, 86B.56 (2022), 12 pp.

Foster Tom

Horizontal-Strip LLT Polynomials

Abstract. Lascoux, Leclerc, and Thibon defined a remarkable family of symmetric functions that are q-deformations of products of skew Schur functions. These LLT polynomials G_λ(x;q) can be indexed by a tuple λ of skew diagrams. When each skew diagram of λ is a row, we define a weighted graph Π(λ) associated to λ. We show that a horizontal-strip LLT polynomial is determined by this weighted graph. When Π(λ) has no triangles, we establish a combinatorial Schur expansion of G_λ(x;q). We also explore a connection to extended chromatic symmetric functions.

Received: November 25, 2021. Accepted: March 4, 2022. Final version: April 1, 2022.

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