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Asymptotically maximal Schubitopes
Jack Chen-An Chou, Linus Setiabrata
We find a layered permutation whose Schubert polynomial has support of size asymptotically at least . This gives precise asympto…
Newton polytopes of fireworks Grothendieck polynomials
Jack Chen-An Chou, Linus Setiabrata
We show that the support of the Grothendieck polynomial of any fireworks permutation is as large as possible: a monomial appears in if and only if i…
Double orthodontia formulas and Lascoux positivity
Linus Setiabrata, Avery St. Dizier
We give a new formula for double Grothendieck polynomials based on Magyar's orthodontia algorithm for diagrams. Our formula implies a similar formula for double Schubert polynomial…
M-convexity of Grothendieck polynomials via bubbling
Elena S. Hafner, Karola Mészáros, Linus Setiabrata +1
We introduce bubbling diagrams and show that they compute the support of the Grothendieck polynomial of any vexillary permutation. Using these diagrams, we show that the support of…
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…
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…
Faces of root polytopes
Linus Setiabrata
We completely characterize the faces of the root polytope combinatorially. Our results specializ…
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…
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…
On the generalized Erdős--Kneser conjecture: proofs and reductions
Jai Aslam, Shuli Chen, Ethan Coldren +2
Alon, Frankl, and Lovász proved a conjecture of Erdős that one needs at least colors to color the -subsets of such that an…