e-positivity conjecture for generalized natural unit interval orders

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Let P(m)P(\mathbf{m}) be the natural unit interval order associated with a sequence m=(m1,m2,m3,n,…,n)\mathbf{m}=(m_1,m_2,m_3,n,\ldots,n), and let GG be its incomparability graph. Let X~G(t)\widetilde{X}_G(t) denote the chromatic quasisymmetric function of GG. Generalized three-parameter e-positivity conjecture. The function X~G(t)\widetilde{X}_G(t) is ee-positive.

This extends the preceding conjectural family by allowing the first three entries of m\mathbf{m} to vary. The source does not specify whether the conjecture has been resolved.

References

Primary source

Angèle M. Foley, Joshua Kazdan, Larissa Kröll, Sofía Martínez Alberga, Oleksii Melnyk and Alexander Tenenbaum, “Spiders and their Kin: An Investigation of Stanley's Chromatic Symmetric Function for Spiders and Related Graphs”, arXiv:1812.03476 (2022).

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