5 problems

Hayashi's conjecture. For every connected quandle with this profile, $l_i$ divides $l_t$ for every $1\leq i\leq t$; equivalently, all right translation maps are regular permutation…

Asymptotic prevalence conjecture. The apparent dominance of entropic tribrackets at small cardinalities is an artifact of the small cardinalities accessible computationally, analog…

Finite quandle coloring conjecture. There exists a finite collection of finite quandles $X_1,\dots,X_n$ such that the tuples

Let $Q$ be a finite connected quandle with elements $1,2,\ldots,n$ naturally ordered, profile $\{1,\ell_1,\ell_2,\ldots,\ell_k\}$, and $1\leq\ell_1\leq\ell_2\leq\cdots\leq\ell_k$.…

Let $Q$ be a non-trivial finite connected quandle with profile $\{1,\ell_1,\ell_2,\ldots,\ell_k\}$, where $1\leq\ell_1\leq\ell_2\leq\cdots\leq\ell_k$ and $k\in\mathbb{N}$. Profile…