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

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.