Grassmannian


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Grassmannian

[¦gräs¦man·ē·ən]
(mathematics)
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This study turned out to be intimately related to the combinatorics of the positive Grassmannian [Po], weakly separated sets [LZ, OPS], cluster algebras [FZ], alcoved polytopes [LP] and triangulations of hypersimplices, as well as other popular topics of current research in combinatorics.
N] obtained by a desingularisation of a subvariety B' of dimension N - 1 of the Grassmannian G(1,N) of lines of [P.
Each cohomology ring of a Grassmannian or flag variety has a basis of Schubert classes indexed by the elements of the corresponding Weyl group.
n], also known as affine Grassmannian permutations, satisfy [omega](1) < [omega](2) < .
These are special cases of positroid subvarieties of the Grassmannian, for whose definition and the following results we refer to Knutson et al.
This is a parabolic analogue of the lift of the QBG to the affine Bruhat order [LS], which is the combinatorial structure underlying Peterson's theorem [P]; the latter equates the Gromov-Witten invariants of finite- dimensional homogeneous spaces with the Pontryagin homology structure constants of Schubert varieties in the affine Grassmannian.
There is a remarkable subset of the real Grassmannian [Gr.
There is a simple bijection between reduced words of a Grassmannian permutation [sigma] and standard Young tableaux of a shape determined by [sigma].
A Grassmannian permutation with descent at d corresponds to a partition [lambda] of length at most d, i.
Permutation tableaux arose in the study of totally nonnegative Grassmannian, see Postnikov (2006).
Such a structure will be called a partial twin Grassmannian.
The quantum cohomology ring of the Grassmannian of k-dimensional planes in [C.