3 citations · 6 across the 5 of their papers we have counts for
15 papers
On the degree of Grothendieck polynomials
Matt Dreyer, Karola Mészáros, Avery St. Dizier
A beautiful degree formula for the Grothendieck polynomials was recently given by Pechenik, Speyer, and Weigandt (2021). We provide an alternative proof of their degree formula, ut…
On the support of Grothendieck polynomials
Karola Mészáros, Linus Setiabrata, Avery St. Dizier
Grothendieck polynomials of permutations were introduced by Lascoux and Schützenberger in 1982 as a set of distinguished representatives for the K-theor…
Principal specialization of dual characters of flagged Weyl modules
Karola Mészáros, Avery St. Dizier, Arthur Tanjaya
Schur polynomials are special cases of Schubert polynomials, which in turn are special cases of dual characters of flagged Weyl modules. The principal specialization of Schur and S…
An orthodontia formula for Grothendieck polynomials
Karola Mészáros, Linus Setiabrata, Avery St. Dizier
We give a new operator formula for Grothendieck polynomials that generalizes Magyar's Demazure operator formula for Schubert polynomials. Our proofs are purely combinatorial, contr…
Lorentzian polynomials from polytope projections
Karola Mészáros, Linus Setiabrata
Lorentzian polynomials, recently introduced by Brändén and Huh, generalize the notion of log-concavity of sequences to homogeneous polynomials whose supports are integer points of…
Logarithmic concavity of Schur and related polynomials
June Huh, Jacob P. Matherne, Karola Mészáros +1
We show that normalized Schur polynomials are strongly log-concave. As a consequence, we obtain Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients in the sp…
Counting integer points of flow polytopes
Kabir Kapoor, Karola Mészáros, Linus Setiabrata
The Baldoni--Vergne volume and Ehrhart polynomial formulas for flow polytopes are significant in at least two ways. On one hand, these formulas are in terms of Kostant partition fu…
Schubert polynomials as projections of Minkowski sums of Gelfand-Tsetlin polytopes
Ricky Ini Liu, Karola Mészáros, Avery St. Dizier
Gelfand-Tsetlin polytopes are classical objects in algebraic combinatorics arising in the representation theory of . The integer point transform of the…
Zero-one Schubert polynomials
Alex Fink, Karola Mészáros, Avery St. Dizier
We prove that if is a pattern of , then we can express the Schubert polynomial as a monomial times (in reindexed variables)…
Root Cones and the Resonance Arrangement
Samuel C. Gutekunst, Karola Mészáros, T. Kyle Petersen
We study the connection between triangulations of a type root polytope and the resonance arrangement, a hyperplane arrangement that shows up in a surprising number of contexts.…
Flow polytopes of partitions
Karola Mészáros, Connor Simpson, Zoe Wellner
Recent progress on flow polytopes indicates many interesting families with product formulas for their volume. These product formulas are all proved using analytic techniques. Our w…
Schubert polynomials as integer point transforms of generalized permutahedra
Alex Fink, Karola Mészáros, Avery St. Dizier
We show that the dual character of the flagged Weyl module of any diagram is a positively weighted integer point transform of a generalized permutahedron. In particular, Schubert a…
From generalized permutahedra to Grothendieck polynomials via flow polytopes
Karola Mészáros, Avery St. Dizier
We study a family of dissections of flow polytopes arising from the subdivision algebra. To each dissection of a flow polytope, we associate a polynomial, called the left-degree po…
Flow polytopes with Catalan volumes
Sylvie Corteel, Jang Soo Kim, Karola Mészáros
The Chan-Robbins-Yuen polytope can be thought of as the flow polytope of the complete graph with netflow vector . The normalized volume of the Chan-Robbins-Y…
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…