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Commutative Properties of Schubert P...

Anderson, Portia Xie,

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Commutative Properties of Schubert Puzzles With Convex Polygonal Boundary Shapes /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Commutative Properties of Schubert Puzzles With Convex Polygonal Boundary Shapes // Portia Xie Anderson.
Author:	Anderson, Portia Xie,
Description:	1 electronic resource (127 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
Contained By:	Dissertations Abstracts International86-12B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32000105
ISBN:	9798283137841

Commutative Properties of Schubert Puzzles With Convex Polygonal Boundary Shapes /
Anderson, Portia Xie,

Commutative Properties of Schubert Puzzles With Convex Polygonal Boundary Shapes /Portia Xie Anderson. - 1 electronic resource (127 pages)

Source: Dissertations Abstracts International, Volume: 86-12, Section: B.

We generalize classical triangular Schubert puzzles to puzzles with convex polygonal boundary. We give these puzzles a geometric Schubert calculus interpretation and derive novel combinatorial commutativity statements, using purely geometric arguments, for puzzles with four, five, and six sides, having various types of symmetry in their boundary conditions. We provide alternate combinatorial proofs as well. We also present formulas for the associated structure constants in terms of Littlewood-Richardson numbers, and we prove an analogue of commutativity for parallelogram-shaped equivariant puzzles. We discuss further extensions of the results to puzzles that perform computations in other cohomology theories, such as K-theory, and 2-step and 3-step puzzles.

English

ISBN: 9798283137841Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Cohomology theories

Commutative Properties of Schubert Puzzles With Convex Polygonal Boundary Shapes /
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100 1 $a Anderson, Portia Xie, $e author. $0 (orcid)0009-0003-4826-8356 $3 3823112
245 1 0 $a Commutative Properties of Schubert Puzzles With Convex Polygonal Boundary Shapes / $c Portia Xie Anderson.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2025
300 $a 1 electronic resource (127 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
500 $a Advisors: Knutson, Allen Committee members: Stillman, Michael; Riley, Tara.
502 $b Ph.D. $c Cornell University $d 2025.
520 $a We generalize classical triangular Schubert puzzles to puzzles with convex polygonal boundary. We give these puzzles a geometric Schubert calculus interpretation and derive novel combinatorial commutativity statements, using purely geometric arguments, for puzzles with four, five, and six sides, having various types of symmetry in their boundary conditions. We provide alternate combinatorial proofs as well. We also present formulas for the associated structure constants in terms of Littlewood-Richardson numbers, and we prove an analogue of commutativity for parallelogram-shaped equivariant puzzles. We discuss further extensions of the results to puzzles that perform computations in other cohomology theories, such as K-theory, and 2-step and 3-step puzzles.
546 $a English
590 $a School code: 0058
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
653 $a Cohomology theories
653 $a Grassmannian
653 $a Schubert calculus
653 $a Schubert puzzle
653 $a Schubert variety
690 $a 0405
690 $a 0642
690 $a 0364
710 2 $a Cornell University. $b Mathematics. $e degree granting institution. $3 3816358
720 1 $a Knutson, Allen $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-12B.
790 $a 0058
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32000105