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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Degrees of symmetric Grothendieck polynomials and Castelnuovo-Mumford regularity
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by Jenna Rajchgot, Yi Ren, Colleen Robichaux, Avery St. Dizier and Anna Weigandt PDF
Proc. Amer. Math. Soc. 149 (2021), 1405-1416 Request permission

Abstract:

We give an explicit formula for the degree of the Grothendieck polynomial of a Grassmannian permutation and a closely related formula for the Castelnuovo-Mumford regularity of the Schubert determinantal ideal of a Grassmannian permutation. We then provide a counterexample to a conjecture of Kummini-Lakshmibai-Sastry-Seshadri on a formula for regularities of standard open patches of particular Grassmannian Schubert varieties and show that our work gives rise to an alternate explicit formula in these cases. We end with a new conjecture on the regularities of standard open patches of arbitrary Grassmannian Schubert varieties.
References
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Additional Information
  • Jenna Rajchgot
  • Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada
  • MR Author ID: 1113184
  • Email: rajchgoj@mcmaster.ca
  • Yi Ren
  • Affiliation: Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, United Kingdom
  • ORCID: 0000-0002-5974-1992
  • Email: yi.ren@chem.ox.ac.uk
  • Colleen Robichaux
  • Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
  • MR Author ID: 1156734
  • ORCID: 0000-0002-8960-1333
  • Email: cer2@illinois.edu
  • Avery St. Dizier
  • Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
  • MR Author ID: 1165589
  • Email: stdizie2@illinois.edu
  • Anna Weigandt
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
  • MR Author ID: 923926
  • Email: weigandt@umich.edu
  • Received by editor(s): December 18, 2019
  • Received by editor(s) in revised form: July 3, 2020
  • Published electronically: January 26, 2021
  • Additional Notes: The first author was partially supported by NSERC Grant RGPIN-2017-05732. The second author was supported by NSERC Grant RGPIN–2017-05732. The third author was supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE 1746047.
  • Communicated by: Patricia L. Hersh
  • © Copyright 2021 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 1405-1416
  • MSC (2010): Primary 13C40, 14N15, 05E40
  • DOI: https://doi.org/10.1090/proc/15294
  • MathSciNet review: 4242300