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pro vyhledávání: '"Williams, Lauren K."'
Autor:
Williams, Lauren K.
The asymmetric simple exclusion process (ASEP) is a model for translation in protein synthesis and traffic flow; it can be defined as a Markov chain describing particles hopping on a one-dimensional lattice. In this article I give an overview of some
Externí odkaz:
http://arxiv.org/abs/2202.00214
Autor:
Moerman, Robert, Williams, Lauren K.
The Exponential Formula allows one to enumerate any class of combinatorial objects built by choosing a set of connected components and placing a structure on each connected component which depends only on its size. There are multiple variants of this
Externí odkaz:
http://arxiv.org/abs/2112.02061
Autor:
Williams, Lauren K.
The positive Grassmannian $Gr_{k,n}^{\geq 0}$ is the subset of the real Grassmannian where all Pl\"ucker coordinates are nonnegative. It has a beautiful combinatorial structure as well as connections to statistical physics, integrable systems, and sc
Externí odkaz:
http://arxiv.org/abs/2110.10856
Autor:
Speyer, David, Williams, Lauren K.
The Dressian and the tropical Grassmannian parameterize abstract and realizable tropical linear spaces; but in general, the Dressian is much larger than the tropical Grassmannian. There are natural positive notions of both of these spaces -- the posi
Externí odkaz:
http://arxiv.org/abs/2003.10231
The study of the moment map from the Grassmannian to the hypersimplex, and the relation between torus orbits and matroid polytopes, dates back to the foundational 1987 work of Gelfand-Goresky-MacPherson-Serganova. On the other hand, the amplituhedron
Externí odkaz:
http://arxiv.org/abs/2002.06164
Publikováno v:
Ann. Inst. Henri Poincar\'e D 7 (2020), no. 3, 303-363
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:
http://arxiv.org/abs/1708.09525
Autor:
Karp, Steven N., Williams, Lauren K.
Publikováno v:
Int. Math. Res. Not. IMRN (2019), no. 5, 1401-1462
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:
http://arxiv.org/abs/1608.08288
Autor:
Williams, Lauren K.
The classical permutohedron Perm is the convex hull of the points (w(1),...,w(n)) in R^n where w ranges over all permutations in the symmetric group. This polytope has many beautiful properties -- for example it provides a way to visualize the weak B
Externí odkaz:
http://arxiv.org/abs/1501.00714
Autor:
Williams, Lauren K.
Cluster algebras are commutative rings with a set of distinguished generators having a remarkable combinatorial structure. They were introduced by Fomin and Zelevinsky in 2000 in the context of Lie theory, but have since appeared in many other contex
Externí odkaz:
http://arxiv.org/abs/1212.6263
Publikováno v:
Advances in Applied Mathematics 46(1--4), 2011, 209--225
In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We illustrate
Externí odkaz:
http://arxiv.org/abs/1005.2696