8 papers
A unit-distance graph in the plane with independence ratio below 1/4
Ãkos 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 ErdÅs. Our proof closely follows th…
Improved bounds for the double cap conjecture
Domonkos Czifra, Ãkos 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 p…
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, Ãkos 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…
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 ErdÅs…