Séminaire Lotharingien de Combinatoire, 89B.33 (2023), 12 pp.

Philippe Nadeau and Vasi Tewari

[Perm_n] via Qsym_n⁺

Abstract. We give a combinatorial interpretation for the expansion of the cohomology class of the permutahedral variety Perm_n in Schubert classes. This requires understanding Schubert polynomials modulo the ideal QSym_n⁺ of positive degree quasisymmetric polynomials. We introduce a new basis for the polynomial ring that we call forest polynomials, together with a bijective correspondence. Both constructions are of independent interest.

Received: November 15, 2022. Accepted: February 20, 2023. Final version: April 1, 2023.

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Séminaire Lotharingien de Combinatoire, 89B.33 (2023), 12 pp.

Philippe Nadeau and Vasi Tewari

[Permn] via Qsymn+

[Perm_n] via Qsym_n⁺