60 citations · 281 across the 30 of their papers we have counts for
5 papers · 1 filter
On an almost all version of the Balog-Szemeredi-Gowers theorem
Xuancheng Shao
We deduce, as a consequence of the arithmetic removal lemma, an almost-all version of the Balog-Szemerédi-Gowers theorem: For any and , there exists $δ=…
Finding linear patterns of complexity one
Xuancheng Shao
We study the following generalization of Roth's theorem for 3-term arithmetic progressions. For s>1, define a nontrivial s-configuration to be a set of s(s+1)/2 integers consisting…
Carries, group theory, and additive combinatorics
Persi Diaconis, Xuancheng Shao, Kannan Soundararajan
Given a group G and a normal subgroup H we study the problem of choosing coset representatives with few carries.
Large values of the additive energy in R^d and Z^d
Xuancheng Shao
Combining Freiman's theorem with Balog-Szemeredi-Gowers theorem one can show that if an additive set has large additive energy, then a large piece of the set is contained in a gene…
Visibility graphs and deformations of associahedra
Satyan L. Devadoss, Rahul Shah, Xuancheng Shao +1
The associahedron is a convex polytope whose face poset is based on nonintersecting diagonals of a convex polygon. In this paper, given an arbitrary simple polygon P, we construct…