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arXiv · 2506.23082

Hall--Littlewood expansions of chromatic quasisymmetric polynomials using linked rook placements

Jang Soo Kim·Seung Jin Lee·Meesue Yoo
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Abstract

In this work, we obtain a Hall--Littlewood expansion of the chromatic quasisymmetric function arising from a natural unit interval order and describe the coefficients in terms of linked rook placements. Applying the Carlsson--Mellit relation between chromatic quasisymmetric functions and unicellular LLT polynomials, we also obtain a combinatorial description for the coefficients of the unicellular LLT polynomials expanded in terms of the modified transformed Hall--Littlewood polynomials.

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Jang Soo Kim, Seung Jin Lee, Meesue Yoo. 2025-06-29. Hall--Littlewood expansions of chromatic quasisymmetric polynomials using linked rook placements. https://arxiv.org/abs/2506.23082

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