Top Posts
Recent comments
 Peter Cameron on New web address
 Peter Cameron on New web address
 dockie73 on New web address
 AMBAT VIJAYAKUMAR on George F. Simmons
 For DeepArcher « Log24 on George F. Simmons
Blogroll
 Astronomy Picture of the Day
 Azimuth
 British Combinatorial Committee
 Comfortably numbered
 Diamond Geezer
 Exploring East London
 From hill to sea
 Gödel's lost letter and P=NP
 Gil Kalai
 Jane's London
 Jon Awbrey
 Kourovka Notebook
 LMS blogs page
 Log24
 London Algebra Colloquium
 London Reconnections
 MathBlogging
 Micromath
 Neill Cameron
 neverendingbooks
 Noncommutative geometry
 numericana hall of fame
 Ratio bound
 Robert A. Wilson's blog
 Since it is not …
 Spitalfields life
 Sylvy's mathsy blog
 SymOmega
 Terry Tao
 The Aperiodical
 The De Morgan Journal
 The ICA
 The London column
 The Lumber Room
 The matroid union
 Theorem of the day
 Tim Gowers
 XKCD
Find me on the web

Join 664 other subscribers
Cameron Counts: RSS feeds
Meta
Tag Archives: symmetric group
A theorem on polytopes
You know what polygons and polyhedra are. How do we extend their study to higher dimensions? There are two parts to this question. The first involves incidence geometry: vertices, edges, faces, etc. Here the generalisation is fairly straightforward. A polygon … Continue reading
Posted in doing mathematics, exposition
Tagged Dimitri Leemans, Maria Elisa Fernandes, regular polytopes, symmetric group, zoom
3 Comments
June
This month, a beautiful formula on an old door panel in Prague. (It may not be very legible in this lowresolution copy.) The formula is for l(Sn), the length of the longest chain of subgroups in the symmetric group Sn. … Continue reading
Chains of semigroups
I have written here about the lovely formula for the length of the longest chain of subgroups in the symmetric group Sn: take n, increase it by 50% (rounding up if necessary), subtract the number of ones in the base … Continue reading
Regular polytopes, 3
In the last two posts on regular polytopes, I gave away something about my method of working. Although I have known about regular polytopes for a long time, I have never attempted to do research on them before. I find … Continue reading
From the archive, 4
A photocopy of a sheet of paper in my handwriting. At the top left, my initials are written in the handwriting of Jaap Seidel. The page begins as follows. Theorem. Let X be a set of points in the ncube … Continue reading
Posted in exposition, history
Tagged cube, Jaap Seidel, Johnson scheme, symmetric group
Leave a comment
The symmetric group, 13
In my post on the Novi Sad Algebraic Conference, I described how the symmetric group on a set X is “contained” in the full transformation semigroup on X, which is itself contained in the clone of functions on X. In … Continue reading
The symmetric group, 12
This instalment is about the maximal subgroups of the symmetric group, and the O’Nan–Scott Theorem. There are two versions of this theorem, one of which is sometimes called the Aschbacher–O’Nan–Scott Theorem. One is about maximal subgroups of the symmetric group … Continue reading
Posted in exposition, symmetric group
Tagged maximal subgroups, O'NanScott theorem, permutation group, symmetric group
6 Comments
The symmetric group, 11
I am going to talk about a celebrated theorem of John Dixon and some of its variants; this is on my mind at the moment, for reasons I will explain at the end. Dixon’s theorem is easily stated. Two random … Continue reading
Posted in exposition, symmetric group, synchronization
Tagged Baire category, Dixon's theorem, symmetric group
4 Comments