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pro vyhledávání: '"Steven N. Karp"'
Autor:
Steven N. Karp
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings, 28th... (2020)
The totally nonnegative Grassmannian Gr≥0 k,n is the set of k-dimensional subspaces V of Rn whose nonzero Plucker coordinates all have the same sign. In their study of scattering amplitudes in N = 4 supersym- metric Yang-Mills theory, Arkani-Hamed
Externí odkaz:
https://doaj.org/article/fecacd3494cd4ac896e3e2ffcce5430a
Autor:
Steven N. Karp
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings, 27th..., Iss Proceedings (2015)
The totally nonnegative Grassmannian is the set of $k$-dimensional subspaces $V$ of ℝ$n$ whose nonzero Plücker coordinates (i.e. $k × k$ minors of a $k × n$ matrix whose rows span $V$) all have the same sign. Total positivity has been much studi
Externí odkaz:
https://doaj.org/article/07c92df23b284975b75f9f8e96885584
Autor:
Anthony M. Bloch, Steven N. Karp
Publikováno v:
Communications in Mathematical Physics. 398:1213-1289
One can view a partial flag variety in $\mathbb{C}^n$ as an adjoint orbit $\mathcal{O}_\lambda$ inside the Lie algebra of $n \times n$ skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a partial flag variety f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0dca1b73e332633682280f8151353537
https://doi.org/10.1007/s00220-022-04540-5
https://doi.org/10.1007/s00220-022-04540-5
Autor:
Anthony M. Bloch, Steven N. Karp
The Toda lattice (1967) is a Hamiltonian system given by $n$ points on a line governed by an exponential potential. Flaschka (1974) showed that the Toda lattice is integrable by interpreting it as a flow on the space of symmetric tridiagonal $n\times
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::475dd66cf19cea7250047c64f96bbcb4
Autor:
Steven N. Karp
Publikováno v:
Journal of Combinatorial Theory, Series A. 145:308-339
The totally nonnegative Grassmannian is the set of $k$-dimensional subspaces $V$ of ℝ$n$ whose nonzero Plücker coordinates (i.e. $k × k$ minors of a $k × n$ matrix whose rows span $V$) all have the same sign. Total positivity has been much studi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::336e5e476c5492009c36c7295021954b
https://doi.org/10.1016/j.jcta.2016.08.003
https://doi.org/10.1016/j.jcta.2016.08.003
Autor:
Steven N. Karp
Publikováno v:
Bulletin of the London Mathematical Society. 52:776-776
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2f8938bad94ff8b3d50680263efd0415
https://doi.org/10.1112/blms.12370
https://doi.org/10.1112/blms.12370
Autor:
Steven N. Karp
We show that for each k and n, the cyclic shift map on the complex Grassmannian Gr(k,n) has exactly $\binom{n}{k}$ fixed points. There is a unique totally nonnegative fixed point, given by taking n equally spaced points on the trigonometric moment cu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::43182b6c93ec0fc65122b370c5827aa2
We prove that three spaces of importance in topological combinatorics are homeomorphic to closed balls: the totally nonnegative Grassmannian, the compactification of the space of electrical networks, and the cyclically symmetric amplituhedron.
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Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::59ad33428c023829e08f63f530c29065
The (tree) amplituhedron A(n,k,m) is the image in the Grassmannian Gr(k,k+m) of the totally nonnegative part of Gr(k,n), under a (map induced by a) linear map which is totally positive. It was introduced by Arkani-Hamed and Trnka in 2013 in order to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::037573bbe4d4a4af0cc69f25ceb33ed6
Autor:
Lauren Williams, Steven N. Karp
The (tree) amplituhedron A(n,k,m) is the image in the Grassmannian Gr(k,k+m) of the totally nonnegative part of Gr(k,n), under a (map induced by a) linear map which is totally positive. It was introduced by Arkani-Hamed and Trnka in 2013 in order to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7c8dd55a305902e17e5a498a4061b68a