Formal Markoff maps are positive

Francois Gueritaud

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Formal Markoff maps are positive

Francois Gueritaud

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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.

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Francois Gueritaud. 2006-05-29. Formal Markoff maps are positive. https://arxiv.org/abs/math/0605735

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