Crew, Pechenik, and Spirkl [9] defined the Kromatic symmetric function \(\overline{X}_G\) as a K-analogue of Stanley’s chromatic symmetric function \(X_G\) [23], and one question they asked was how \(\overline{X}_G\) expands in their \(\overline{p}_\lambda \) basis, which they defined as a K-analogue of the classic power sum basis \(p_\lambda .\) We gave a formula in [21] that partially answered this question, but did not explain the combinatorial significance of the coefficients. Here, we give combinatorial descriptions for the \(\overline{p}\) -coefficients of \(\overline{X}_G\) and \(\omega (\overline{X}_G)\) , lifting the p-expansion of \(X_G\) in terms of acyclic orientations that was given by Bernardi and Nadeau in [6]. We also propose an alternative K-analogue \(\overline{p}'\) of the p-basis that gives slightly cleaner expansion formulas. Our expansions are based on Lyndon heaps, introduced by Lalonde [16], which are representatives for certain equivalence classes of acyclic orientations on clan graphs of G. Additionally, we show that knowing \(\overline{X}_G\) is equivalent to knowing the multiset of independence polynomials of induced subgraphs of G, which gives shorter proofs of all our results from [22] that \(\overline{X}_G\) can be used to determine the number of copies in G of certain induced subgraphs. We also give power sum expansions for the Kromatic quasisymmetric function \(\overline{X}_G(q)\) defined by Marberg in [18] in the case where G is the incomparability graph of a unit interval order.
