9 citations · 24 across the 14 of their papers we have counts for
17 papers
Sums of Weighted Lattice Points of Polytopes
Jesús A. De Loera, Laura Escobar, Nathan Kaplan +1
We study the problem of counting lattice points of a polytope that are weighted by an Ehrhart quasi-polynomial of a family of parametric polytopes. As applications one can compute…
Enumeration of max-pooling responses with generalized permutohedra
Laura Escobar, Patricio Gallardo, Javier González-Anaya +3
We investigate the combinatorics of max-pooling layers, which are functions that downsample input arrays by taking the maximum over shifted windows of input coordinates, and which…
Hessenberg varieties of codimension one in the flag variety
Laura Escobar, Martha Precup, John Shareshian
We study geometric and topological properties of Hessenberg varieties of codimension one in the type A flag variety. Our main results: (1) give a formula for the Poincaré polynomia…
Partial permutohedra
Roger E. Behrend, Federico Castillo, Anastasia Chavez +4
Partial permutohedra are lattice polytopes which were recently introduced and studied by Heuer and Striker. For positive integers and , the partial permutohedron $\mathcal{P…
Complexity of the usual torus action on Kazhdan-Lusztig varieties
Maria Donten-Bury, Laura Escobar, Irem Portakal
We investigate the class of Kazhdan-Lusztig varieties, and its subclass of matrix Schubert varieties, endowed with a naturally defined torus action. Writing a matrix Schubert varie…
A graph coloring approach to family-based haplotype reconstruction
Jason A. Anema, Laura Escobar
Edge Constrained Vertex Coloring (ECVC) problems are defined on a finite multigraph, their solutions are characterized, and a linear time algorithm is given for solving ECVCs o…
Which Schubert Varieties are Hessenberg Varieties?
Laura Escobar, Martha Precup, John Shareshian
After proving that every Schubert variety in the full flag variety of a complex reductive group is a general Hessenberg variety, we show that not all such Schubert varieties ar…
Gröbner bases, symmetric matrices, and type C Kazhdan-Lusztig varieties
Laura Escobar, Alex Fink, Jenna Rajchgot +1
We study a class of combinatorially-defined polynomial ideals which are generated by minors of a generic symmetric matrix. Included within this class are the symmetric determinanta…
The harmonic polytope
Federico Ardila, Laura Escobar
We study the harmonic polytope, which arose in Ardila, Denham, and Huh's work on the Lagrangian geometry of matroids. We describe its combinatorial structure, showing that it is a…
Wall-crossing for Newton-Okounkov bodies and the tropical Grassmannian
Laura Escobar, Megumi Harada
Tropical geometry and the theory of Newton-Okounkov bodies are two methods which produce toric degenerations of an irreducible complex projective variety. Kaveh-Manon showed that t…
K-orbit closures and Barbasch-Evens-Magyar varieties
Laura Escobar, Benjamin J. Wyser, Alexander Yong
We define the Barbasch-Evens-Magyar varieties. We show they are isomorphic to the smooth varieties defined in [D.~Barbasch-S.~Evens '94] that map generically finitely to symmetric…
Newton polytopes and symmetric Grothendieck polynomials
Laura Escobar, Alexander Yong
Symmetric Grothendieck polynomials are inhomogeneous versions of Schur polynomials that arise in combinatorial -theory. A polynomial has saturated Newton polytope (SNP) if every…
The multidegree of the multi-image variety
Laura Escobar, Allen Knutson
The multi-image variety is a subvariety of Gr(1,P^3)^n that models taking pictures with n rational cameras. We compute its cohomology class in the cohomology of Gr(1,P^3)^n, and fr…
Rhombic tilings and Bott-Samelson varieties
Laura Escobar, Oliver Pechenik, Bridget Eileen Tenner +1
S.~Elnitsky (1997) gave an elegant bijection between rhombic tilings of -gons and commutation classes of reduced words in the symmetric group on letters. P.~Magyar (1998) f…
Toric matrix Schubert varieties and their polytopes
Laura Escobar, Karola Meszaros
Given a matrix Schubert variety , it can be written as (where is maximal possible). We characterize when is toric…
Subword complexes via triangulations of root polytopes
Laura Escobar, Karola Mészáros
Subword complexes are simplicial complexes introduced by Knutson and Miller to illustrate the combinatorics of Schubert polynomials and determinantal ideals. They proved that any s…
Brick manifolds and toric varieties of brick polytopes
Laura Escobar
Bott-Samelson varieties are a twisted product of 's with a map into . These varieties are mostly studied in the case in which the map into is bir…