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The Schubert calculus

2010
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? The last century saw the development of a calculus for solving this problem and a large number of examples were worked out by Schubert, after whom
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Affine Schubert Calculus

2014
This chapter discusses how k-Schur and dual k-Schur functions can be defined for all types. This is done via some combinatorial problems that come from the geometry of a very large family of generalized flag varieties. They apply to the expansion of products of Schur functions, k-Schur functions and their dual basis, and Schubert polynomials.
Thomas Lam   +5 more
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Numerical Schubert Calculus by the Pieri Homotopy Algorithm

SIAM Journal on Numerical Analysis, 2002
Summary: Based on Pieri's formula on Schubert varieties [see \textit{F. Sottile}, Can. J. Math. 49, 1281-1298 (1997; Zbl 0933.14031)], the Pieri homotopy algorithm was first proposed by \textit{B. Huber, F. Sottile}, and \textit{B. Sturmfels} [J. Symb. Comput.
Tien-Yien Li, Xiaoshen Wang, Mengnien Wu
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An arithmetic Schubert calculus

1995
Let \({\mathbb{G}}(n,p)\) be the Grassmann variety of \(p\)-dimensional subspaces of an \(n\)-dimensional space over \(\text{Spec } \mathbb{Z}\). It is shown that the Chow-Arakelov ring of \({\mathbb{G}}(n,p)\) is isomorphic to the ring \({\mathcal A}(p,n)\), where \({\mathcal A}(p,n)\) is defined as follows.
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Schubert Calculus

The American Mathematical Monthly, 1972
S. L. Kleiman, Dan Laksov
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A combinatorial rule for (co)minuscule Schubert calculus

Advances in Mathematics, 2009
Hugh Thomas, Alexander Yong
exaly  

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