Normalisers of primitive permutation groups in quasipolynomial time

Primitive normalisers in quasipolynomial time

The normaliser problem has as input two subgroups $H$ and $K$ of the symmetric group $S_n$, and asks for a generating set for $N_K(H)$: it is not known to have a subexponential time solution. It is proved in [Roney-Dougal & Siccha, 2020] that if $H$ is primitive then the normaliser problem can be solved in quasipolynomial time. We show that for all subgroups $H$ and $K$ of $S_n$, in quasipolynomial time we can decide whether $N_{S_n}(H)$ is primitive, and if so compute $N_K(H)$. Hence we reduce the question of whether one can solve the normaliser problem in quasipolynomial time to the case whe…

Hamming 三明治

Hamming sandwiches

本文构造了度 n 的原始结合方案（Hamming 三明治），其自同构数至少为 exp(n^{1/8})，反驳了 Babai 猜想，并修正该猜想以限制非 Schur 原始相干构型的自同构数量。

关于距离正则图的自同构群

On the automorphism group of a distance-regular graph

本文证明直径至少为3的距离正则图（除Johnson、Hamming和crown图外）的活动度至少为Cn/(log n)^6，并由此给出原始距离正则图自同构群边传递作用时的拟多项式上界，证明不依赖有限单群分类。