Alexander Xue

most citedBalanced convex partitions of lines in the plane

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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.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…