Markov numbers of semigroups
Combinatorics
2026-04-21 v1 Number Theory
Abstract
In this paper, we systematically study generalized Markov numbers arising from semigroups of reduced integer matrices. This construction allows us to find these numbers by counting perfect matchings of a new family of bipartite graphs, which we call wug-snake graphs. We also show how this relates to the geometry of numbers and the classical theory of Markov minima.
Cite
@article{arxiv.2604.17069,
title = {Markov numbers of semigroups},
author = {Oleg Karpenkov and Yefei Ma},
journal= {arXiv preprint arXiv:2604.17069},
year = {2026}
}
Comments
49 pages