27 citations · 48 across the 8 of their papers we have counts for
6 papers · 1 filter
Covering triangular grids with multiplicity
Abdul Basit, Alexander Clifton, Paul Horn
Motivated by classical work of Alon and Füredi, we introduce and address the following problem: determine the minimum number of affine hyperplanes in needed to cover…
Improved bounds on a generalization of Tuza's conjecture
Abdul Basit, Daniel McGinnis, Henry Simmons +2
For an -uniform hypergraph , let denote the maximum size of a set~ of edges in such that every two edges in intersect in less than vertices, and l…
Zarankiewicz's problem for semilinear hypergraphs
Abdul Basit, Artem Chernikov, Sergei Starchenko +2
A bipartite graph with is semilinear if for some and the edge relation consists of th…
On the independent set sequence of a tree
Abdul Basit, David Galvin
Alavi, Malde, Schwenk and Erdős asked whether the independent set sequence of every tree is unimodal. Here we make some observations about this question. We show that for the unifo…
An improved sum-product bound for quaternions
Abdul Basit, Ben Lund
We show that there exists an absolute constant , such that, for any finite set of quaternions, \[ \max\{|A+A, |AA| \} \gtrsim |A|^{4/3 + c}. \] This generalizes a sum-pr…
On the number of ordinary lines determined by sets in complex space
Abdul Basit, Zeev Dvir, Shubhangi Saraf +1
Kelly's theorem states that a set of points affinely spanning must determine at least one ordinary complex line (a line passing through exactly two of the points…