### Top Posts

### Recent comments

- Robin Chapman on Orthogonal arrays and codes over rings
- Peter Cameron on Orthogonal arrays and codes over rings
- Robin Chapman on Orthogonal arrays and codes over rings
- Jon Awbrey on Data science and statistics
- Ross Graham on Mathematics and religion?

### Blogroll

- Annoying precision
- Astronomy Picture of the Day
- Azimuth
- Bad science
- Bob Walters
- British Combinatorial Committee
- CIRCA tweets digest
- CoDiMa
- Coffee, love, and matrix algebra
- Computational semigroup theory
- DC's Improbable Science
- Diamond Geezer
- Exploring East London
- Gödel's lost letter and P=NP
- Gil Kalai
- Haris Aziz
- Intersections
- Jane's London
- Jon Awbrey
- LMS blogs page
- Log24
- London Algebra Colloquium
- London Reconnections
- Machines like us
- Marie Cameron's blog
- MathBlogging
- Micromath
- Neill Cameron
- neverendingbooks
- Noncommutative geometry
- numericana hall of fame
- Paul Goldberg
- Robert A. Wilson's blog
- Sheila's blog
- Since it is not …
- Spitalfields life
- St Albans midweek lunch
- Stubborn mule
- SymOmega
- Terry Tao
- The Aperiodical
- The De Morgan Journal
- The London column
- The Lumber Room
- The matroid union
- Theorem of the day
- Tim Gowers
- XKCD

### Find me on the web

### Cameron Counts: RSS feeds

### Meta

# Tag Archives: permutation groups

## Permutation groups and transformation semigroups

When I first decided to apply to the LMS to run a Durham symposium on Permutation Groups and Transformation Semigroups, I had a fairly clear idea of what I wanted: topics (both finite and infinite) where the techniques and results … Continue reading

## Real v recreational mathematics

A footnote to my report on Persi Diaconis’ lecture on Martin Gardner. Persi challenged us to consider the question: Is there a sharp division between “real” mathematics and “recreational” mathematics, and if so, where does it come? G. H. Hardy clearly thought … Continue reading

Posted in exposition
Tagged Bill Kantor, G. H. Hardy, perfect shuffles, permutation groups, Persi Diaconis, Ron Graham
Leave a comment

## A thrifty algorithm

Two important classical parameters of a permutation group G of degree n are the base size, the smallest size of a collection of points whose pointwise stabiliser is the identity; and the minimal degree, the smallest number of points moved … Continue reading

Posted in exposition, open problems
Tagged base size, greedy algorithm, Kenneth Blaha, minimal degree, permutation groups, primitive groups
4 Comments

## A permutation group challenge, 2

The result in the preceding post can be formulated as follows: A permutation group of degree n = 2k which is transitive on partitions of shape (k,k) but not on ordered partitions of this shape, has a fixed point and is (k−1)-homogeneous … Continue reading

## A permutation group challenge

Long ago, in the distant past before the Classification of Finite Simple Groups, Peter Neumann, Jan Saxl and I investigated the class of permutation groups acting on sets of even cardinality n = 2k, with the following interchange property: Any subset of … Continue reading

Posted in exposition, open problems
Tagged CFSG, homogeneity, permutation groups, semigroups
1 Comment

## Synchronizing coherent configurations

In previous posts I have discussed coherent configurations and synchronization. Yesterday I realised that these two topics can be combined … Synchronization A (finite-state, deterministic) automaton consists of a finite set of states and a finite set of transitions, each … Continue reading

Posted in exposition, history
Tagged Boris Weisfeiler, coherent configurations, permutation groups, synchronization
Leave a comment

## Permutation groups and regular semigroups

This week, I gave a talk in the Pure Mathematics seminar explaining what João Araújo and I have been up to this summer. I will try to summarise here. João believes that semigroup theorists have shied away from studying the … Continue reading