8 papers
Bolzano: Case Studies in LLM-Assisted Mathematical Research
Martin Balko, Jan GrebÃk, Pavel HubáÄek +5
We report new results on eight problems in mathematics and theoretical computer science, produced with the assistance of Bolzano, an open-source multi-agent LLM system. Bolzano orc…
Massively Parallel Proof-Number Search for Impartial Games and Beyond
Tomáš ÄÞek, Martin Balko, Martin Schmid
Proof-Number Search is a best-first search algorithm with many successful applications, especially in game solving. As large-scale computing clusters become increasingly accessible…
Characterisation of the big Ramsey degrees of the generic partial order
Martin Balko, David Chodounský, Natasha Dobrinen +4
As a result of 33 intercontinental Zoom calls, we characterise big Ramsey degrees of the generic partial order. This is an infinitary extension of the well known fact that finite p…
On forbidden configurations in point-line incidence graphs
Martin Balko, Nóra Frankl
The celebrated Szemerédi--Trotter theorem states that the maximum number of incidences between points and lines in the plane is , which is asymptotically tight…
Crossing and non-crossing families
Todor AntiÄ, Martin Balko, Birgit Vogtenhuber
For a finite set of points in the plane in general position, a \emph{crossing family} of size in is a collection of line segments with endpoints in that are pai…
Faces in rectilinear drawings of complete graphs
Martin Balko, Anna Brötzner, Fabian Klute +1
We initiate the study of extremal problems about faces in convex rectilinear drawings of~, that is, drawings where vertices are represented by points in the plane in convex po…