Finite combinatorics and computability theory
Combinatorics
2026-04-21 v1 Logic
Abstract
We prove that the existence of finite combinatorial objects such as affine planes, mutually orthogonal Latin squares, and resolvable balanced incomplete block designs can be reformulated as the existence of certain algorithmic reductions between problems related to the pigeonhole principle. We then study the latter using counting arguments and computability theory. In particular, we demonstrate that computability theoretic techniques can be used to refine and prove new results in finite combinatorics.
Keywords
Cite
@article{arxiv.2604.18290,
title = {Finite combinatorics and computability theory},
author = {Damir D. Dzhafarov and Jun le Goh},
journal= {arXiv preprint arXiv:2604.18290},
year = {2026}
}