3 problems

Let $t$ be a rational number, let $\tilde w_t(A,B)$ be the corresponding Christoffel word, and let $\hat A$ and $\hat B$ be the displayed $y$-deformed generators. Write … Let $F_t$…

Let $\mu:\\{\mathtt{0},\mathtt{1}\\}^*\to\mathrm{SL}_2(\mathbb{Z})$ be the monoid homomorphism defined by … A Christoffel word is a word over $\\{\mathtt{0},\mathtt{1}\\}$ in the u…

Conjecture. These inequalities hold for all $k$ for which they are defined; namely, $M_{k+1}\geq M_k$ and $M_{k+1}\leq M_k+M_{k-1}$ for all $k\geq 2$.