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Shareshian–Wachs elementary positivity
Resolves the elementary-positivity part of the Shareshian–Wachs conjecture: the chromatic quasisymmetric function of every natural unit interval graph has elementary-basis coefficients in . The coefficients count explicitly described permutations, giving a combinatorial explanation of positivity.
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Elementary positivity of chromatic quasisymmetric functions
Sep 24, 2026·paper.pdf
We prove that the chromatic quasisymmetric function of every natural unit interval graph is elementary-positive over . This resolves the elementary-positivity part of the Shareshian–Wachs conjecture.