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Tag Archives: permutation group
Orthogonal block structures
If you google “commuting equivalence relations” you will find signs of a large and rich literature. I want to talk about one aspect, on the border of algebraic combinatorics and experimental design: orthogonal block structures. Look up orthogonal block structures … Continue reading
Posted in doing mathematics, exposition
Tagged association scheme, partition lattice, permutation group, statistics
1 Comment
A problelm
Given a finite permutation group G on a set X, the permutation character π of G is the function on G mapping an element g to its number of fixed points in X. This is a character of G, the … Continue reading
A problem
Since I have been saying rather a lot about association schemes and coherent configurations lately, I thought I would mention an open problem. This is probably one for the experts, and I guess it has been ignored because of the … Continue reading
Posted in open problems
Tagged association scheme, coherent configuration, permutation group
8 Comments
Imprimitive permutations in primitive groups
Asymptotics of permutation counts is a subject with a long history. The result that the proportion of permutations which are derangements (that is, have no fixed points) is very close to 1/e is one of the oldest results in enumerative … Continue reading
Posted in exposition
Tagged imprimitive, permutation, permutation group, primitive, Wielandt's conjecture
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Three versus four
The title is homage to the Gödel’s Last Letter and P=NP blog, which a week ago had a post entitled Two versus three. At the problem session at the Banff meeting last night, Dugald Macpherson and Andras Pongracz posed various … Continue reading
Computational group theory, 1
Computational group theory is the art or science of using a computer to learn something about a group. I was introduced to it by John Cannon in the early 1980s. It seems like a black art to many mathematicians (myself … Continue reading
Posted in exposition
Tagged Bill Kantor, black-box group, Laszlo Babai, permutation group, presentation
1 Comment
Groups, lattices and bases
About ten years ago I wrote a six-page paper, which I didn’t succeed in getting any journal editor to publish. I will say a bit about its contents below, but you can read it now: I have posted it on … 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'Nan-Scott theorem, permutation group, symmetric group
6 Comments
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