Results 51 to 60 of about 220,490 (165)
Lagrangian Geometry Towards Type AxC Schubert Calculus
, 2023 59 pagesKnutson and Zinn-Justin gave a geometric explanation of the Knutson-Tao puzzle rule for computing Schubert calculus of certain partial flag varieties in type A .
Keese, Hannah
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Schubert Calculus and the Homology of the Peterson Variety [PDF]
The Electronic Journal of Combinatorics, 2015 We use the tight correlation between the geometry of the Peterson variety and the combinatorics the symmetric group to prove that homology of the Peterson variety injects into the homology of the flag variety. Our proof counts the points of intersection between certain Schubert varieties in the full flag variety and the Peterson variety, and shows that
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A Positive Formula for Type A Peterson Schubert Calculus
La Matematica, 2022 48 pages, significant edits for ...
Rebecca Goldin, Brent Gorbutt
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, 1979 An enumerative problem asks the following type of question; how many figures (lines, planes, conies, cubics, etc.) meet transversely (or are tangent to) a certain number of other figures in general position?
Higham, David Paul
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Schubert Calculus: An Algebraic Introduction [PDF]
, 2005 Schubert Calculus on Grassmannians can be performed on all grassmannians at once, empowering its computational efficiency, via derivations on an exterior algebra of a free module of countable rank.
Gatto, Letterio
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A formalism for equivariant Schubert calculus
, 2009 In previous work we have developed a general formalism for Schubert calculus. Here we show how this theory can be adapted to give a formalism for equivariant Schubert calculus consisting of a basis theorem, a Pieri formula and a Giambelli formula.
Laksov, Dan,
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Fibered Quadratic Hopf Algebras Related to Schubert Calculus [PDF]
, 2000 We introduce and study certain quadratic Hopf algebras related to Schubert calculus of the flag ...
Procesi, Claudio, Fomin, Sergey
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Generalized permutahedra and Schubert calculus
, 2020 We connect generalized permutahedra with Schubert calculus. Thereby, we give sufficient vanishing criteria for Schubert intersection numbers of the flag variety.
Dizier, Avery St., Yong, Alexander
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Positivity of Peterson Schubert calculus
Advances in MathematicsTo appear in Advances in Mathematics. 31 pages, 1 table. Modifications: - Expanded introduction; - Improved explanation of the equivariant naturality of Peterson varieties; - Modified Theorem 1.1 to make explicit the positive integrality of pairing; - Added corollary and remark to make explicit extension to integral cohomology (Cor 3.8, Rmk 3.9 ...
Goldin, Rebecca +2 more
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, 2012 In this paper we study the T-equivariant generalized cohomology of flag varieties using two models, the Borel model and the moment graph model. We study the differences between the Schubert classes and the Bott-Samelson classes. After setup of the general framework we compute, for classes of Schubert varieties of complex dimension <4 in rank 2 ...
Ganter, Nora, Ram, Arun
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