1 code implementation • 10 Oct 2019 • Samuel Ferguson, Nat Sothanaphan
We describe computer programs accompanying our paper and show that running them suffices to verify Fuglede's conjecture in $\mathbb{Z}_2^5$ and $\mathbb{Z}_2^6$.
Classical Analysis and ODEs Discrete Mathematics Combinatorics
1 code implementation • 9 Apr 2019 • Sam Ferguson, Azita Mayeli, Nat Sothanaphan
As an application, we obtain new weak evidence in favor of the open problem by giving a sequence of subsets of finite abelian groups whose tightness quantities go to infinity in the limit.
Combinatorics Classical Analysis and ODEs Number Theory 43A70, 43A40 (Primary), 52C22, 11L07 (Secondary)
1 code implementation • 25 Jan 2019 • Samuel Ferguson, Nat Sothanaphan
We show, however, that our method does not extend to $\mathbb{Z}_{p}^{3}$.
Number Theory Classical Analysis and ODEs 43A15, 43A40, 43A70, 43A75
1 code implementation • 22 May 2018 • Nat Sothanaphan
We prove that for a symmetric, strictly log-convex density on the real line, there are four possible types of perimeter-minimizing triple bubbles.
Metric Geometry 49Q10
1 code implementation • 13 Sep 2017 • Eliot Bongiovanni, Alejandro Diaz, Arjun Kakkar, Nat Sothanaphan
We determine the least-area unit-volume tetrahedral tile of Euclidean space, without the constraint of Gallagher et al. that the tiling uses only orientation-preserving images of the tile.
Metric Geometry
no code implementations • 2 Jun 2015 • Weerachai Neeranartvong, Jonathan Novak, Nat Sothanaphan
In this paper, we construct an injection $A \times B \rightarrow M \times M$ from the product of any two nonempty subsets of the symmetric group into the square of their midpoint set, where the metric is that corresponding to the conjugacy class of transpositions.
Combinatorics Metric Geometry
