Given a finite permutation group G with domain Ω, we associate two subsets of natural
numbers to G, namely I (G, Ω) and M (G, Ω), which are the sets of cardinalities of all the …

In this thesis, we study three problems. First, we determine new bounds for base sizes b (G,
Ω) of primitive subspace actions of finite almost simple classical groups G. Such base sizes …

Let G be a permutation group, acting on a set\varOmega Ω of size n. A subset BB
of\varOmega Ω is a base for G if the pointwise stabilizer G_ (B) G (B) is trivial. Let b (G) be …

We show that if G is a primitive subgroup of S⁡ n that is not large base, then any irredundant
base for G has size at most 5 log⁡ n. This is the first logarithmic bound on the size of an …

With the advancement of global positioning systems and communication technologies,
location‐based services (LBS) have become widely used. However, user location privacy is …

Let 𝐺 be a finite permutation group on Ω. An ordered sequence (ω 1,…, ω ℓ) of elements of
Ω is an irredundant base for 𝐺 if the pointwise stabilizer is trivial and no point is fixed by the …

Irredundant bases for finite groups of Lie type Page 1 Pacific Journal of Mathematics
IRREDUNDANT BASES FOR FINITE GROUPS OF LIE TYPE NICK GILL AND MARTIN W …

The maximal size of a minimal generating set Page 1 Forum of Mathematics, Sigma (2023), Vol.
11:e70 1–10 doi:10.1017/fms.2023.71 RESEARCH ARTICLE The maximal size of a minimal …

We study the natural action of S n on the set of k-subsets of the set {1,…, n} when 1≤ k≤ n
2. For this action we calculate the maximum size of a minimal base, the height and the …

A base for a finite permutation group $ G\le\mathrm {Sym}(\Omega) $ is a subset of $\Omega
$ with trivial pointwise stabiliser in $ G $, and the base size of $ G $ is the smallest size of a …