9 problems

Uniform boundedness conjecture. There exists an absolute constant $c$ such that $\rho_0(G)<c$ for all finite primitive permutation groups $G$. This conjecture asserts that the larg…

Stanley's conjecture. For $n\geq4$ and $n\geq5$, respectively,

Let $C_n$ be the $n$th Catalan number, and let $d_n$ be the number of derangements among the $123$-avoiding permutations of length $n$. The source considers an asymptotic form…

Derangement proportion conjecture. The following formulas hold:

Alternating-group derangement bound conjecture. The following hold:

Derangement-class product conjecture. There exist conjugacy classes $C$ and $D$ of derangements such that

Almost simple fixer-ratio conjecture. We have

Let $G$ be a primitive permutation group of degree $n$, and let $D(G)$ be the subgroup generated by the derangements in $G$. A Frobenius group is a transitive permutation group who…

Density conjecture. The set $\mathcal{A}_r$ is infinite. Moreover,