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coherent monotone paths 1exponential lower bounds 1Hirsch conjecture 1linear programming 1polytopes 1shadow simplex method 1

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math.CO2026

Any Proof of Polynomial Hirsch Must be Completely Incoherent

Alexander E. Black, Lei Xue

The paper constructs families of polytopes for which every coherent monotone path induced by a linear function has exponential length, disproving a polynomial‑Hirsch‑type conjectur…

math.CO2026

Saturation for Non-Symmetric Macdonald Polynomials

Milo Bechtloff Weising, Alexander E. Black

We prove that supports of non-symmetric Macdonald polynomials are -convex. As a consequence, we resolve a 2019 conjecture of Monical, Tokcan, and Yong that they have the saturat…