10 papers
Permutahedra, Lusztig varieties, degenerations, and subdivisions
Allen Knutson, Mario Sanchez, Melissa Sherman-Bennett
We present an embedded (in ) degeneration of Lusztig varieties (which generalize type Hessenberg varieties) to certain unions of Richardson varieties, giving a simultaneou…
Persistent Subdivisions of Coxeter Permutahedra
Timothy Blanton, Jesús A. De Loera, Melissa Sherman-Bennett
We investigate the realizations of Coxeter permutahedra which are also Coxeter matroid polytopes; these are polytopes of the form where is a…
Unexpected toric Richardson varieties
Eugene Gorsky, Soyeon Kim, Melissa Sherman-Bennett
We prove that an open Richardson variety in the complete flag variety for is isomorphic to a torus if and only if the corresponding closed Richardson variety is tor…
Large induced acyclic and outerplanar subgraphs of 2-outerplanar graph
Glencora Borradaile, Hung Le, Melissa Sherman-Bennett
Albertson and Berman conjectured that every planar graph has an induced forest on half of its vertices. The best known lower bound, due to Borodin, is that every planar graph has a…
Plabic Tangles and Cluster Promotion Maps
Chaim Even-Zohar, Matteo Parisi, Melissa Sherman-Bennett +2
Inspired by the BCFW recurrence for tilings of the amplituhedron, we introduce the general framework of `plabic tangles' that utilizes plabic graphs to define rational maps between…
A dimer view on Fox's trapezoidal conjecture
Karola Mészáros, Melissa Sherman-Bennett, Alexander Vidinas
Fox's conjecture (1962) states that the sequence of absolute values of the coefficients of the Alexander polynomial of alternating links is trapezoidal. While the conjecture remain…