7 problems

Saturation conjecture. The terms that appear in the numerator of a Markov polynomial $M_{\rho}$ are precisely those corresponding to the integer lattice points in the Newton polygo…

Let $b/a=[a_1,a_2,\dots,a_n]$ be the continued-fraction expansion of the rational number $b/a$, and let $A_m,B_m$ be the corresponding penultimate-continuant vertices of the Markov…

Markov Sail Duality conjecture. The coefficients of Markov polynomials satisfy these two Markov-sail duality identities. This would determine almost all interior sail coefficients…

Let $\rho=a/b$ be rational, and let the critical triangle be the set of lattice points satisfying … Consider the coefficients of the Markov polynomial associated with these lattice…

Let $M_\rho$ be a Markov polynomial, and let its coefficients be regarded as weights on the corresponding Newton polygon. A sequence is log-concave when $x_k^2\geq x_{k-1}x_{k+1}$…

Saturation conjecture. The terms appearing in the numerator of $M_\rho$ are precisely those corresponding to the integer lattice points in $\Delta_\rho$. The conjecture is an equiv…

Let $X,Y,Z\in\mathbb Z[x^{\pm1},y^{\pm1},z^{\pm1}]$ be integer Laurent polynomials satisfying equation … in terms of the Markov-polynomial construction; the source gives no resolut…