7 papers
Consequences of Dependent Dividing on Burden
Yuki Takahashi
If has dependent dividing, then the burden agrees with the dp-rank witnessed by NIP formulas. We use this observation to prove that if has dependent dividing, then the burd…
Graphs with prescribed radius, diameter, and center
Kelly Guest, Andrew Johnson, Peter Johnson +3
Among other things, it is shown that for every pair of positive integers , , satisfying , and every finite simple graph there is a connected graph with…
Lifting methods in mass partition problems
Pablo Soberón, Yuki Takahashi
Many results in mass partitions are proved by lifting to a higher-dimensional space and dividing the higher-dimensional space into pieces. We extend such methods to…
Diophantine property of matrices and attractors of projective iterated function systems in
Boris Solomyak, Yuki Takahashi
We prove that almost every finite collection of matrices in and with positive entries is Diophantine. Next we restrict ourselves to the case $…
Sums of two self-similar Cantor sets
Yuki Takahashi
We show that for any pair of self-similar Cantor sets with sum of Hausdorff dimensions greater than 1, one can create an interval in the sumset by applying arbitrary small perturba…
On the interior of projections of planar self-similar sets
Yuki Takahashi
We consider projections of planar self-similar sets, and show that one can create nonempty interior in the projections by applying arbitrary small perturbations, if the self-simila…