Combinatorial Theory

We prove that two horizontal-strip LLT polynomials are equal if the associated weighted graphs defined by the author in a previous paper are isomorphic. This provides a sufficient condition for equality of horizontal-strip LLT polynomials and yields a well-defined LLT polynomial indexed by a weighted graph. We use this to prove some new relations between LLT polynomials and we explore a connection with extended chromatic symmetric functions.

Mathematics Subject Classifications: 05E05, 05E10, 05C15

Keywords: Chromatic symmetric function, LLT polynomial, Hall-Littlewood polynomial, interval graph, Schur function, weighted graph