3 problems

Pairing-matrix conjecture. If the generators $a_1,\ldots,a_n$ and $b_1,\ldots,b_m$ of $\Gamma_C$ are distinct, then $\Gamma_C$ contains a nontrivial element of finite order. This i…

Bellaterra expander conjecture. The Bellaterra graphs $\{B_i\}_{i=1}^\infty$ are a family of two-sided expanders. The authors' computations suggest an eigenvalue gap of roughly…

Let a reversible Mealy automaton be a Mealy automaton whose transition maps are permutations, and let the semigroup generated by an automaton be the semigroup generated by its stat…