17 citations · 33 across the 12 of their papers we have counts for
13 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…
Quantitative Transversal Theorems in the Plane
Ilani Axelrod-Freed, João Pedro Carvalho, Yuki Takahashi
Hadwiger's theorem is a Helly-type theorem involving common transversals to families of convex sets instead of common intersections. Subsequently, Pollack and Wenger identified a n…
Frobenius templates in certain matrix rings
Timothy Eller, Jakub Kraus, Yuki Takahashi +1
The classical Frobenius problem is to find the largest integer that cannot be written as a linear combination of a given set of positive, coprime integers using nonnegative integer…
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…
Sums of two homogeneous Cantor sets
Yuki Takahashi
We show that for any two homogeneous Cantor sets with sum of Hausdorff dimensions that exceeds 1, one can create an interval in the sumset by applying arbitrary small perturbations…
Products of two Cantor sets
Yuki Takahashi
We consider products of two Cantor sets, and obtain the optimal estimates in terms of their thickness that guarantee that their product is an interval. This problem is motivated by…
Quantum and Spectral Properties of the Labyrinth Model
Yuki Takahashi
We consider the Labyrinth model, which is a two-dimensional quasicrystal model. We show that the spectrum of this model, which is known to be a product of two Cantor sets, is an in…
Graphs emerging from the solutions to the periodic discrete Toda equation over finite fields
Masataka Kanki, Yuki Takahashi, Tetsuji Tokihiro
The periodic discrete Toda equation defined over finite fields has been studied. We obtained the finite graph structures constructed by the network of states where edges denote pos…
Mixed spectral regimes for square Fibonacci Hamiltonians
Jake Fillman, Yuki Takahashi, William Yessen
For the square tridiagonal Fibonacci Hamiltonian, we prove existence of an open set of parameters which yield mixed interval-Cantor spectra (i.e. spectra containing an interval as…