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no. 4
Sums of Schubert structure constants with bounded Coxeter length
Stelzer, Ada Mead1
1University of Illinois Urbana–Champaign, Dept. of mathematics, 1305 W. Green St., Urbana, IL 61801 (USA)
Algebraic Combinatorics, Volume 9 (2026) no. 4, pp. 893-900

Pak–Robichaux recently introduced a signed puzzle rule for Schubert structure constants, which they use to show that sums $\gamma _k(n)$ of these constants with a bounded number of inversions are polynomial. We give a different, conceptual proof that $\gamma _k(n)$ is (eventually) polynomial, which computes its lead term and extends to all classical Lie types.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.497
Classification: 14N15, 05E10, 05E05
Keywords: Schubert calculus, Lie theory, equivariant restriction

Stelzer, Ada Mead  1

1 University of Illinois Urbana–Champaign, Dept. of mathematics, 1305 W. Green St., Urbana, IL 61801 (USA)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Stelzer, Ada Mead. Sums of Schubert structure constants with bounded Coxeter length. Algebraic Combinatorics, Volume 9 (2026) no. 4, pp. 893-900. doi: 10.5802/alco.497
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[1] Andersen, H. H.; Jantzen, J. C.; Soergel, W. Representations of quantum groups at a $p$th root of unity and of semisimple groups in characteristic $p$: independence of $p$, Astérisque (1994) no. 220, p. 321 | MR | Numdam | Zbl

[2] Billey, Sara C. Kostant polynomials and the cohomology ring for ${G}/{B}$, Duke Math. J., Volume 96 (1999) no. 1, pp. 205-224 | DOI | MR | Zbl

[3] Goresky, Mark; Kottwitz, Robert; MacPherson, Robert Equivariant cohomology, Koszul duality, and the localization theorem, Invent. Math., Volume 131 (1998) no. 1, pp. 25-83 | DOI | MR | Zbl

[4] Pak, Igor; Robichaux, Colleen Signed puzzles for Schubert coefficients, 2025 (forthcoming, Algebr. Comb.) | arXiv

[5] Richmond, Edward; Slofstra, William The isomorphism problem for Schubert varieties, 2022 | arXiv

[6] Robichaux, Colleen; Yadav, Harshit; Yong, Alexander The $\rm {A}{\cdot }{B}{\cdot }{C}{\cdot }{Ds}$ of Schubert calculus, Sém. Lothar. Combin., Volume 85 (2020), Paper no. B85a, 12 pages | MR

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