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19982022
most citedImproved lower bound on the size of Kakeya sets over finite fields

13 citations · 27 across the 11 of their papers we have counts for

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math.CO2009

Extensions to the Method of Multiplicities, with applications to Kakeya Sets and Mergers

Zeev Dvir, Swastik Kopparty, Shubhangi Saraf +1

We extend the "method of multiplicities" to get the following results, of interest in combinatorics and randomness extraction. (A) We show that every Kakeya set (a set of points th…

math.CO2008★ 4 cited

Testing Linear-Invariant Non-Linear Properties

Arnab Bhattacharyya, Victor Chen, Madhu Sudan +1

We consider the task of testing properties of Boolean functions that are invariant under linear transformations of the Boolean cube. Previous work in property testing, including th…

math.CO2008★ 13 cited

Improved lower bound on the size of Kakeya sets over finite fields

Shubhangi Saraf, Madhu Sudan

In a recent breakthrough, Dvir showed that every Kakeya set in $\F^n$ must be of cardinality at least $c_n |\F|^n$ where . We improve this lower bound to $β^n |\F…