142 citations · 752 across the 110 of their papers we have counts for
9 papers · 1 filter
The independence number of the Birkhoff polytope graph, and applications to maximally recoverable codes
Daniel Kane, Shachar Lovett, Sankeerth Rao
Maximally recoverable codes are codes designed for distributed storage which combine quick recovery from single node failure and optimal recovery from catastrophic failure. Gopalan…
Asymptotic Results for the Queen Packing Problem
Daniel M Kane
We consider the problem of placing k queens on an nxn board so that the total number of attacked squares is as small as possible. In particular, we consider the domain where k is s…
An example concerning set addition in F_2^n
Ben Green, Daniel Kane
We construct sets in a vector space over with the property that is "statistically" almost closed under addition by in the sense that almost al…
A bound on partitioning clusters
Daniel Kane, Terence Tao
Let be a finite collection of sets (or "clusters"). We consider the problem of counting the number of ways a cluster can be partitioned into two disjoint clusters $A_…
Central Limit Theorems for some Set Partition Statistics
Bobbie Chern, Persi Diaconis, Daniel M. Kane +1
We prove the conjectured limiting normality for the number of crossings of a uniformly chosen set partition of [n] = {1,2,...,n}. The arguments use a novel stochastic representatio…
On the Crossing Number of Complete Graphs with an Uncrossed Hamiltonian Cycle
Daniel M. Kane
We prove new lower bounds on the crossing number of a complete graphs assuming that it is drawn in such a way that it contains a Hamiltonian cycle with no crossings.