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pro vyhledávání: '"Bennett, Melissa"'
The set of perfect matchings of a connected bipartite plane graph $G$ has the structure of a distributive lattice, as shown by Propp, where the partial order is induced by the height of a matching. In this article, our focus is the dimer face polynom
Externí odkaz:
http://arxiv.org/abs/2408.11156
The amplituhedron $A_{n,k,m}$ is a geometric object introduced in the context of scattering amplitudes in $N=4$ super Yang Mills. It generalizes the positive Grassmannian (when $n=k+m$), cyclic polytopes (when $k=1$), and the bounded complex of the c
Externí odkaz:
http://arxiv.org/abs/2404.03026
Autor:
Even-Zohar, Chaim, Lakrec, Tsviqa, Parisi, Matteo, Tessler, Ran, Sherman-Bennett, Melissa, Williams, Lauren
The amplituhedron is a mathematical object which was introduced to provide a geometric origin of scattering amplitudes in $\mathcal{N}=4$ super Yang Mills theory. It generalizes \emph{cyclic polytopes} and the \emph{positive Grassmannian}, and has a
Externí odkaz:
http://arxiv.org/abs/2402.15568
Autor:
Even-Zohar, Chaim, Lakrec, Tsviqa, Parisi, Matteo, Tessler, Ran, Sherman-Bennett, Melissa, Williams, Lauren
The amplituhedron $A_{n,k,m}(Z)$ is the image of the positive Grassmannian $Gr_{k,n}^{\geq 0}$ under the map ${Z}: Gr_{k,n}^{\geq 0} \to Gr_{k,k+m}$ induced by a positive linear map $Z:\mathbb{R}^n \to \mathbb{R}^{k+m}$. Motivated by a question of Ho
Externí odkaz:
http://arxiv.org/abs/2310.17727
First, this article develops the theory of weaves and their cluster structures for the affine cones of positroid varieties. In particular, we explain how to construct a weave from a reduced plabic graph, show it is Demazure, compare their associated
Externí odkaz:
http://arxiv.org/abs/2308.06184
We show that braid varieties for any complex simple algebraic group $G$ are cluster varieties. This includes open Richardson varieties inside the flag variety $G/B$.
Comment: 29 pages. v2: minor changes
Comment: 29 pages. v2: minor changes
Externí odkaz:
http://arxiv.org/abs/2301.07268
Leclerc constructed a conjectural cluster structure on Richardson varieties in simply laced types using cluster categories. We show that in type A, his conjectural cluster structure is in fact a cluster structure. We do this by comparing Leclerc's co
Externí odkaz:
http://arxiv.org/abs/2210.13302
We introduce $3$-dimensional generalizations of Postnikov's plabic graphs and use them to establish cluster structures for type $A$ braid varieties. Our results include known cluster structures on open positroid varieties and double Bruhat cells, and
Externí odkaz:
http://arxiv.org/abs/2210.04778
Publikováno v:
In Advances in Mathematics June 2024 447
