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Peer-reviewedCC BY 4.0Algebraic Combinatorics

Signed puzzles for Schubert coefficients

  • Igor Pak1
  • Colleen Robichaux2
  1. 1University of California, Los Angeles, Department of Mathematics, 520 Portola Plaza, Los Angeles, CA 90095 (USA)
  2. 2University of California, Davis, One Shields Ave., Mathematical Science Building, Davis, CA 95616 (USA)
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Abstract

We give a signed puzzle rule to compute Schubert coefficients. The rule is based on a careful analysis of Knutson’s recurrence [12]. We use the rule to prove polynomiality of the sums of Schubert coefficients with bounded number of inversions.

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Cite

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BibTeX
@article{pak2026signed,
  title = {{Signed puzzles for Schubert coefficients}},
  author = {Igor Pak and Colleen Robichaux},
  journal = {Algebraic Combinatorics},
  year = {2026},
  month = oct,
  doi = {10.5802/alco.517},
  url = {https://alco.centre-mersenne.org/articles/10.5802/alco.517/},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Signed puzzles for Schubert coefficients
AU  - Igor Pak
AU  - Colleen Robichaux
PY  - 2026
DA  - 2026/10/27
JO  - Algebraic Combinatorics
DO  - 10.5802/alco.517
UR  - https://alco.centre-mersenne.org/articles/10.5802/alco.517/
AB  - We give a signed puzzle rule to compute Schubert coefficients. The rule is based on a careful analysis of Knutson’s recurrence [12]. We use the rule to prove polynomiality of the sums of Schubert coefficients with bounded number of inversions.
SN  - 2589-5486
ER  -