4 problems

Let $Q$ and $Q'$ be symplectic quandles of the same dimension over the ring $\mathbb{Z}_n$. They are isomorphism–isometry conjecture. Isomorphic as quandles if and only if they are…

Let $Q$ be a finite quandle, and let $qp_Q(s,t)$ denote its quandle polynomial. A quandle is Latin when its operation is left-invertible, in addition to the right-invertibility req…

A finite rack $X$ has profile $1^{m_0}l_1^{m_1}l_2^{m_2}\cdots l_k^{m_k}$ when its inner automorphism has $m_0$ cycles of length $1$, $m_1$ cycles of length $l_1$, and so on. Hayas…

Let $n\geq 3$. A quandle of cyclic type is a quandle whose cardinality is $n$ and whose associated structure has cyclic type as defined in the paper. Prime-power cardinality conjec…