6 papers · 1 filter
A tight bound for affine-linearity, via universal ballot matrices
Apoorva Khare, Ashwin Sah
Based on work with Greenfeld and with Ziegler, Tao showed a concatenation result that if a map is affine-linear on every line parallel to the coor…
A central limit theorem for the matching number of a sparse random graph
Margalit Glasgow, Matthew Kwan, Ashwin Sah +1
In 1981, Karp and Sipser proved a law of large numbers for the matching number of a sparse ErdÅs-Rényi random graph, in an influential paper pioneering the so-called differential…
Quasipolynomial bounds on the inverse theorem for the Gowers -norm
James Leng, Ashwin Sah, Mehtaab Sawhney
We prove quasipolynomial bounds on the inverse theorem for the Gowers -norm. The proof is modeled after work of Green, Tao, and Ziegler and uses as a crucial input rece…
Anticoncentration in Ramsey graphs and a proof of the ErdÅs-McKay conjecture
Matthew Kwan, Ashwin Sah, Lisa Sauermann +1
An -vertex graph is called -Ramsey if it has no clique or independent set of size (i.e., if it has near-optimal Ramsey behavior). In this paper, we study edge-sta…
Enumerating Matroids and Linear Spaces
Matthew Kwan, Ashwin Sah, Mehtaab Sawhney
We show that the number of linear spaces on a set of points and the number of rank-3 matroids on a ground set of size are both of the form , where $c=e^{…
High-Girth Steiner Triple Systems
Matthew Kwan, Ashwin Sah, Mehtaab Sawhney +1
We prove a 1973 conjecture due to ErdÅs on the existence of Steiner triple systems with arbitrarily high girth.