24 citations · 51 across the 13 of their papers we have counts for
13 papers
Resolution of Erdős Problem #728: a writeup of Aristotle's Lean proof
Nat Sothanaphan
We provide a writeup of a resolution of Erdős Problem #728; this is the first Erdős problem (a problem proposed by Paul Erdős which has been collected in the Erdős Problems website…
An improved lower bound to Erdos' problem concerning products of distances for fixed diameter
Nat Sothanaphan
Erdos, Herzog and Piranian asked whether, for points in the plane with fixed diameter (maximum distance between points), an arrangement of a regular -gon maximizes their pro…
Irregular Stanley sequences plausibly do not have growth
Nat Sothanaphan
Stanley sequences starting from the set where is a positive integer have long been conjectured to be divided into two types: the "regular" type where the growth rate…
Riesz bases of exponentials and multi-tiling in finite abelian groups
Sam Ferguson, Azita Mayeli, Nat Sothanaphan
Motivated by the open problem of exhibiting a subset of Euclidean space which has no exponential Riesz basis, we focus on exponential Riesz bases in finite abelian groups. We point…
Fuglede's conjecture fails in 4 dimensions over odd prime fields
Samuel Ferguson, Nat Sothanaphan
Fuglede's conjecture in , a prime, says that a subset tiles by translation if and only if is spectral, meaning any complex-valu…
Double Bubbles on the Line with Log-convex Density with Bounded
Nat Sothanaphan
We extend results of Bongiovanni et al. on double bubbles on the line with log-convex density to the case where the derivative of the log of the density is bounded. We show that th…
Naive Bayesian Learning in Social Networks
Jerry Anunrojwong, Nat Sothanaphan
The DeGroot model of naive social learning assumes that agents only communicate scalar opinions. In practice, agents communicate not only their opinions, but their confidence in su…
Determinants of Block Matrices with Noncommuting Blocks
Nat Sothanaphan
Let be an matrix over a commutative ring . Divide into blocks. Assume that the blocks commute pairwise. Consider the following two procedures:…
1D Triple Bubble Problem with Log-Convex Density
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. This extends the work of Bongiova…
Isoperimetry in Surfaces of Revolution with Density
Eliot Bongiovanni, Alejandro Diaz, Arjun Kakkar +1
The isoperimetric problem with a density or weighting seeks to enclose prescribed weighted volume with minimum weighted perimeter. According to Chambers' recent proof of the log-co…
The Least-Area Tetrahedral Tile of Space
Eliot Bongiovanni, Alejandro Diaz, Arjun Kakkar +1
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 t…
Double Bubbles on the Real Line with Log-Convex Density
Eliot Bongiovanni, Leonardo Di Giosia, Alejandro Diaz +6
The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in is the standard double bubble. We seek the opti…
A Curved Brunn-Minkowski Inequality for the Symmetric Group
Weerachai Neeranartvong, Jonathan Novak, Nat Sothanaphan
In this paper, we construct an injection from the product of any two nonempty subsets of the symmetric group into the square of their midpoint s…