Séminaire Lotharingien de Combinatoire, 95B.1 (2026), 12 pp.

Alexander E. Black and Milo Bechtloff Weising

Saturation for Non-symmetric Macdonald Polynomials

Abstract. We prove that supports of non-symmetric Macdonald polynomials are M-convex. As a consequence, we resolve a 2019 conjecture of Monical, Tokcan, and Yong that they have the saturated Newton polytope property. As a further consequence, we prove that the moment polytopes of affine Schubert varieties in the affine Grassmannian of type GL are generalized permutahedra.

Received: November 15, 2025. Accepted: February 15, 2026. Final version: April 1, 2026.

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