6 papers
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…
Heronian friezes
Sergey Fomin, Linus Setiabrata
Motivated by computational geometry of point configurations on the Euclidean plane, and by the theory of cluster algebras of type A, we introduce and study Heronian friezes, the Eu…
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…
Fair splittings by independent sets in sparse graphs
Alexander Black, Umur Cetin, Florian Frick +2
Given a partition of the vertex set of a graph, we are interested in finding multiple disjoint independent sets that contain the correct fr…
Splitting loops and necklaces: Variants of the square peg problem
Jai Aslam, Shujian Chen, Florian Frick +3
Toeplitz conjectured that any simple planar loop inscribes a square. Here we prove variants of Toeplitz' square peg problem. We prove Hadwiger's 1971 conjecture that any simple loo…