Lauren K. Williams

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Lauren Williams (joint work with Einar Steingrímsson) We introduce and study a class of tableaux which we call permutation tableaux; these tableaux are naturally in bijection with permutations, and they are a distinguished subset of the " Le-diagrams " of Alex Postnikov. The structure of these tableaux is in some ways more transparent than the structure of(More)
Postnikov [7] has given a combinatorially explicit cell decomposition of the totally nonnegative part of a Grassmannian, denoted Gr k,n , and showed that this set of cells is isomorphic as a graded poset to many other interesting graded posets. The main result of our work is an explicit generating function which enumerates the cells in Gr k,n according to(More)
We introduce some combinatorial objects called staircase tableaux, which have cardinality 4(n)n!, and connect them to both the asymmetric exclusion process (ASEP) and Askey-Wilson polynomials. The ASEP is a model from statistical mechanics introduced in the late 1960s, which describes a system of interacting particles hopping left and right on a(More)
In this paper we study the partially ordered set Q of cells in Rietsch’s [20] cell decomposition of the totally nonnegative part of an arbitrary flag variety P ≥0 . Our goal is to understand the geometry of P ≥0 : Lusztig [13] has proved that this space is contractible, but it is unknown whether the closure of each cell is contractible, and whether P ≥0 is(More)
Introduced in the late 1960’s [33, 43], the asymmetric exclusion process (ASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites. It has been cited as a model for traffic flow and protein synthesis. In the most general form of the ASEP with open(More)