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Horizontal-strip LLT polynomials


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_\lambda(x;q) can be indexed by a tuple \lambda of skew diagrams. When each skew diagram is a row, we define a weighted graph \Pi(\lambda). We show that a horizontal-strip LLT polynomial is determined by this weighted graph. When \Pi(\lambda) has no triangles, we establish a combinatorial Schur expansion of G_\lambda(x;q). We also explore a connection to extended chromatic symmetric functions.

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