10 problems

A bi-Perron number is an algebraic integer $\beta>1$ whose Galois conjugates all lie in the annulus $\beta^{-1}<|z|<\beta$, with $\beta^{-1}$ also among its conjugates. Fried's con…

Even-odd monotonicity conjecture. For all $k\geq 1$,

Odd-genus normalized liminf conjecture.

Minimal accumulation point conjecture. The minimal accumulation point of this set is $\sigma^2$.

Exact minimal stretch factor conjecture. The normalized stretch factor of $f$ is greater than or equal to the largest real root of

Odd-genus normalized limit conjecture.

Odd-genus orientation-reversing stretch factor conjecture. For all $k\geq 2$, $\delta^+_{\mathrm{rev}}(S_{2k-1})$ is the largest root of

Genus 9 and 11 minimal stretch factor conjecture. The minimal stretch factors and minimal polynomials are predicted to be

Minimal polynomial conjecture. For all $k\geq 2$, $\delta^+(N_{2k})$ is the largest root of

Let the cities be the points $\{(i,j): i,j\in\mathbb{Z}\}$ in the plane, and consider a Steiner network on this square-grid configuration. Its normalized length is its total networ…