Alexander Xue

most citedBalanced convex partitions of lines in the plane

1 citations · 1 across the 2 of their papers we have counts for

collaborators

3 papers

math.CO2024

Polymatroids are to finite groups as matroids are to finite fields

Ed Swartz, Prairie Wentworth-Nice, Alexander Xue

Given a subgroup $H$ of a product of finite groups $G = i = 1 \prod n Γ_{i}$ and $b > 1,$ we define a polymatroid $P (H, b) .$ If all of the $Γ_…

math.MG2019★ 1 cited

Balanced convex partitions of lines in the plane

Alexander Xue, Pablo Soberón

We prove an extension of a ham sandwich theorem for families of lines in the plane by Dujmović and Langerman. Given two sets $A, B$ of $n$ lines each in the plane, we prove that it…

math.CO2019

Quantitative combinatorial geometry for concave functions

Sherry Sarkar, Alexander Xue, Pablo Soberón

We prove several exact quantitative versions of Helly's and Tverberg's theorems, which guarantee that a finite family of convex sets in $R^{d}$ has a large intersection. Our results…