Formal Markoff maps are positive
Number Theory
2007-05-23 v1 Combinatorics
Abstract
This note defines a family of Laurent polynomials (indexed in the rational projective line) which generalize the Markoff numbers and relate to the character variety of the one-cusped torus. We describe which monomials appear in each polynomial and prove all the coefficients are positive integers. We also conjecture a generalization of that positivity result.
Cite
@article{arxiv.math/0605735,
title = {Formal Markoff maps are positive},
author = {Francois Gueritaud},
journal= {arXiv preprint arXiv:math/0605735},
year = {2007}
}
Comments
12 pages, 3 figures