22 citations · 43 across the 6 of their papers we have counts for
5 papers · 1 filter
Bergman Complexes, Coxeter Arrangements, and Graph Associahedra
Federico Ardila, Victor Reiner, Lauren Williams
Tropical varieties play an important role in algebraic geometry. The Bergman complex B(M) and the positive Bergman complex B+(M) of an oriented matroid M generalize to matroids the…
Permutation Tableaux and Permutation Patterns
Einar Steingrimsson, Lauren K. Williams
In this paper 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 distinguish…
The Positive Bergman Complex of an Oriented Matroid
Federico Ardila, Caroline Klivans, Lauren Williams
We study the positive Bergman complex B+(M) of an oriented matroid M, which is a certain subcomplex of the Bergman complex B(M) of the underlying unoriented matroid. The positive B…
The tropical totally positive Grassmannian
David Speyer, Lauren K. Williams
Tropical algebraic geometry is the geometry of the tropical semiring (R, min, +). The theory of total positivity is a natural generalization of the study of matrices with all minor…
Enumeration of totally positive Grassmann cells
Lauren K. Williams
Alex Postnikov has given a combinatorially explicit cell decomposition of the totally nonnegative part of a Grassmannian, denoted Gr_{kn}+, and showed that this set of cells is iso…