Bogdan C. Dumitru

collaborators

4 papers

math.CO2025

Notes on the 33-point Erdős--Szekeres problem

Bogdan Dumitru

The determination of $E S (7)$ is the first open case of the planar Erdős--Szekeres problem, where the general conjecture predicts $E S (7) = 33$ . We present a SAT encoding for the 33-po…

math.CO2025

Two-colorings of finite grids: variations on a theorem of Tibor Gallai

Bogdan Dumitru, Mihai Prunescu

A celebrated but non-effective theorem of Tibor Gallai states that for any finite set $A$ of $Z^{n}$ and for any finite number of colors $c$ there is a minimal $m$ such that no colo…

cs.FL2025

A Sharper Upper Bound for the Separating Words Problem

Bogdan C. Dumitru

We show that for any two distinct words $s_{1}, s_{2}$ over an arbitrary alphabets, there exists a deterministic finite automaton with $O (lo g^{2} n)$ states that accepts $s_{1}$ and…

math.NT2025

Notes on the Finiteness of Powers of Two with All Even Digits

Bogdan C. Dumitru

We study the problem of finding positive integers $n$ such that all the decimal digits of $2^{n}$ are even, i.e., belong to ${0, 2, 4, 6, 8}$ . Computational checks up to $n = 10^{1…