Bogdan C. Dumitru

collaborators

10 papers

math.NT2026

Straight-line programs for the solutions of Pell's equation

Bogdan Dumitru, Mihai Prunescu

For nonsquare $d \geq 2$ , we construct fixed straight-line programs for the least non-trivial solution $(X_{1}, Y_{1})$ of $x^{2} - d y^{2} = 1$ , using addition, truncated subtraction, multiplicat…

math.CO2026

Towards a more structured search for Erdős-Gyárfás counter-examples

Guillaume Ducoffe, Bogdan Dumitru

The Erdős-Gyárfás conjecture posits that every graph with minimum degree at least three contains a cycle of length some power of two. We prove a few simple structural properties fo…

math.CO2026

Sunflower-Free Uniform Families: Recursive Constructions and Explicit Bounds

Edward Axante, Cristian Budala, David Chitic +2

Let $f (w, k)$ be the maximum size of a $w$ -uniform family containing no sunflower with $k$ petals. We introduce a recursive construction for sunflower-free families and use it to ob…

math.NT2026

Short arithmetic terms for the cardinality of elliptic curves over rings of remainder classes and over finite fields

Bogdan Dumitru, Mihai Prunescu

Arithmetic terms are fixed finite compositions of addition, truncated subtraction, multiplication, integer division and exponentiation on natural numbers. We construct such terms f…

math.CO2026

An Exhaustive Census of Main-Diagonal Symmetric Costas Arrays of Orders 37-42

Bogdan Dumitru, Cristian Budala

We determine by exhaustive enumeration all main-diagonal symmetric Costas arrays of orders 37 through 42. There are 4 arrays of order 37, none of order 38, 16 of order 39, 2 of ord…

math.CO2026

Alternating Extremes in Graceful Labelings of Full Binary Trees and Spider Trees

Bogdan Dumitru, Mihai Nacu

We study a pinned form of graceful labeling. For full binary trees, we ask whether some deepest root-to-leaf path can carry the alternating extreme pattern $0, n - 1, 1, n - 2, \dots$ . Suc…

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…