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Generalized Permutahedra and Schubert Calculus

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Abstract

We connect generalized permutahedra with Schubert calculus. Thereby, we give sufficient vanishing criteria for Schubert intersection numbers of the flag variety. Our argument utilizes recent developments in the study of Schubitopes, which are Newton polytopes of Schubert polynomials. The resulting tableau test executes in polynomial time.

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Acknowledgements

We would like to thank Husnain Raza for writing code, as part of the Illinois Combinatorics Lab for Undergraduate Experience (ICLUE) program, to help study Knutson’s descent cycling. We would also like to thank our collective authors Anshul Adve, Alex Fink, Karola Mészáros, Cara Monical, Neriman Tokcan, and Colleen Robichaux from [1, 7, 16] for their work upon which is paper is possible. AS was supported by an NSF postdoctoral fellowship. AY was partially supported by a Simons Collaboration Grant, an NSF RTG 1937241 in Combinatorics, and an appointment at the UIUC Center for Advanced Study.

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  1. Department of Mathematics, U. Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Avery St. Dizier & Alexander Yong

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  1. Avery St. Dizier
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  2. Alexander Yong
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Correspondence to Avery St. Dizier.

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Dizier, A.S., Yong, A. Generalized Permutahedra and Schubert Calculus. Arnold Math J. 8, 517–533 (2022). https://doi.org/10.1007/s40598-022-00208-z

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