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Title: Degrees of symmetric Grothendieck polynomials and Castelnuovo-Mumford regularity
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 ofarbitraryGrassmannian Schubert varieties.  more » « less
Award ID(s):
2002079
PAR ID:
10546541
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
American Mathematical Society
Date Published:
Journal Name:
Proceedings of the American Mathematical Society
Volume:
149
Issue:
742
ISSN:
0002-9939
Page Range / eLocation ID:
1405 to 1416
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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