8 papers
A unit-distance graph in the plane with independence ratio below 1/4
Ákos Dúcz, Dániel Varga
We prove that there exists a finite unit-distance graph in the plane with independence ratio strictly smaller than 1/4, answering a question of Erdős. Our proof closely follows the…
Improved bounds for the double cap conjecture
Domonkos Czifra, Ákos Dúcz, Máté Matolcsi +2
In 1974, Witsenhausen asked for the maximum possible density of a measurable subset of the unit sphere such that contains no pa…
The Structure of Relation Decoding Linear Operators in Large Language Models
Miranda Anna Christ, Adrián Csiszárik, Gergely Becsó +1
This paper investigates the structure of linear operators introduced in Hernandez et al. [2023] that decode specific relational facts in transformer language models. We extend thei…
On the density of Kravitz sets
Vsevolod Lev, Máté Matolcsi, Péter Pál Pach +1
We show that for a subset of the cyclic group of prime order , if the sumset is not the whole group, then . Besides combinatorial arguments, we…
Triplets of Mutually Unbiased Bases
Máte Matolcsi, Ákos K. Matszangosz, Dániel Varga +1
We initiate a systematic study of triplets of mutually unbiased bases (MUBs). We show that in each MUB-triplet is characterized by a object that…
Piercing intersecting convex sets
Imre Bárány, Travis Dillon, Dömötör Pálvölgyi +1
Assume two finite families and of convex sets in have the property that for every and $B\in \math…
Diverse beam search to find densest-known planar unit distance graphs
Peter Engel, Owen Hammond-Lee, Yiheng Su +2
This paper addresses the problem of determining the maximum number of edges in a unit distance graph (UDG) of vertices using computer search. An unsolved problem of Paul Erdős…
The fractional chromatic number of the plane is at least 4
Máté Matolcsi, Imre Z. Ruzsa, Dániel Varga +1
We prove that the fractional chromatic number of the unit distance graph of the Euclidean plane is greater than or equal to . Interestingly, however, we canno…