Results 21 to 30 of about 36,312 (298)
Total positivity for the Lagrangian Grassmannian [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The positroid decomposition of the Grassmannian refines the well-known Schubert decomposition, and has a rich combinatorial structure. There are a number of interesting combinatorial posets which index positroid varieties,just as Young diagrams index ...
Rachel Karpman
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Affine type A geometric crystal structure on the Grassmannian [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We construct a type A(1) n−1 affine geometric crystal structure on the Grassmannian Gr(k, n). The tropicalization of this structure recovers the combinatorics of crystal operators on semistandard Young tableaux of rectangular shape (with n − k rows ...
Gabriel Frieden
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Integral geometry on discrete matrices
Moroccan Journal of Pure and Applied Analysis, 2021 In this note, we study the Radon transform and its dual on the discrete matrices by defining hyperplanes as being infinite sets of solutions of linear Diophantine equations. We then give an inversion formula and a support theorem.
Attioui Abdelbaki
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Total positivity for cominuscule Grassmannians [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 In this paper we explore the combinatorics of the non-negative part $(G/P)_{\geq 0}$ of a cominuscule Grassmannian. For each such Grassmannian we define Le-diagrams ― certain fillings of generalized Young diagrams which are in bijection with the cells of
Thomas Lam, Lauren Williams
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Combinatorics of Positroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Recently Postnikov gave a combinatorial description of the cells in a totally-nonnegative Grassmannian. These cells correspond to a special class of matroids called positroids.
Suho Oh
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Cube-Split: A Structured Grassmannian Constellation for Non-Coherent SIMO Communications [PDF]
IEEE Transactions on Wireless Communications, 2019 In this paper, we propose a practical structured constellation for non-coherent communication with a single transmit antenna over Rayleigh flat and block fading channel without instantaneous channel state information.
K. Ngo +3 more
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A Combinatorial Approach to Multiplicity-Free Richardson Subvarieties of the Grassmannian [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We consider Buch's rule for K-theory of the Grassmannian, in the Schur multiplicity-free cases classified by Stembridge. Using a result of Knutson, one sees that Buch's coefficients are related to Möbius inversion. We give a direct combinatorial proof of
Michelle Snider
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K-classes for matroids and equivariant localization [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 To every matroid, we associate a class in the K-theory of the Grassmannian. We study this class using the method of equivariant localization. In particular, we provide a geometric interpretation of the Tutte polynomial.
Alex Fink, David Speyer
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Cluster structures in Schubert varieties in the Grassmannian [PDF]
Proceedings of the London Mathematical Society, 2019 In this article we explain how the coordinate ring of each (open) Schubert variety in the Grassmannian can be identified with a cluster algebra, whose combinatorial structure is encoded using (target labelings of) Postnikov's plabic graphs.
K. Serhiyenko +2 more
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Restricted Secant Varieties of Grassmannians [PDF]
Collectanea Mathematica (2023): 1-21, 2022 Restricted secant varieties of Grassmannians are constructed from sums of points corresponding to $k$-planes with the restriction that their intersection has a prescribed dimension. We study dimensions of restricted secant of Grassmannians and relate them to the analogous question for secants of Grassmannians via an incidence variety construction.
arxiv +1 more source