2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112948This 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.12 pages, 3 figuresNumber TheoryCombinatorics11B57; 52C99text