OpenAI research collection · 1 manuscript · Source checked 2026-10-19
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 \mathbb N[q]. The coefficients count explicitly described permutations, giving a combinatorial explanation of positivity.
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We prove that the chromatic quasisymmetric function of every natural unit interval graph is elementary-positive over \mathbb N[q]. This resolves the elementary-positivity part of the Shareshian–Wachs conjecture.
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