3 problems

Connected idempotent shelf polynomial conjecture. If $S$ is idempotent, then

Let $S$ be a shelf, with its operation and connectedness defined in the paper. A shortest-cycle characterization of connected shelves. There exists a shortest cycle that covers all…

Let $(X,\operatorname{\star})$ be a shelf, with distributive homology groups $H_n(X)$ and rank denoted by $\operatorname{rk}$. Rank Growth Conjecture. For $n\geqslant |X|-2$, one h…