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Tag Archives: partitions
The geometry of diagonal groups
This is an interim report on ongoing work with Rosemary Bailey, Cheryl Praeger and Csaba Schneider. We have reached a point where we have a nice theorem, even though there is still a lot more to do before the project … Continue reading
Posted in doing mathematics, exposition
Tagged Cartesian lattices, diagonal groups, partitions
8 Comments
The existential transversal property
One of the first things that João Araújo introduced me to when we started collaborating, after synchronization, was the universal transversal property: a permutation group G on the set {1,…,n} has the kuniversal transversal property (kut for short) if, given … Continue reading
Posted in exposition
Tagged partitions, permutation groups, regular semigroups, transversals
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A puzzle for you
The Petersen graph is perhaps the most famous graph of all. It has ten vertices, fifteen edges, valency 3, and no triangles. Since the complete graph on ten vertices has 45 edges and valency 9, one might ask whether the … Continue reading
Partition homogeneity
This post discusses a paper by Jorge André, João Araújo and me, which has just been accepted for the Journal of Algebra. There is a slight tangle to the history of this paper, which I want to describe. First a … Continue reading
Posted in exposition, history
Tagged homogeneity, partitions, semigroups, symmetric groups, transitivity
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G. C. Steward lectures 2008
While I was uploading lecture notes, I also put on the page the notes from my G. C. Steward lectures at Gonville and Caius College in 2008. You can find them here. I spent the first half of 2008 in … Continue reading
Posted in history, Lecture notes, Neill Cameron artwork
Tagged automata, bagali polo, Euler, Latin squares, line graphs, magic squares, Moebius inversion, OEIS, Online Encyclopedia of Integer Sequences, parking functions, partitions, root systems, statistics, Sudoku, synchronization, Tehran
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A cliff
The “combinatorial explosion” is a wellknown phenomenon. I recently came across a very dramatic example of it. I was trying to compute the function F(n,k), defined to be the maximum of S×P, over all sets S of ksubsets and all … Continue reading
Posted in exposition
Tagged combinatorial explosion, computers, GAP, GRAPE, Leonard Soicher, partitions, subsets, transversals
4 Comments
Combinatorics Ancient and Modern
Towards the end of 2011, I posted a paper on the arXiv with the title “Aftermath”. A correspondent wondered if this was a Borgesian game, the final chapter to a nonexistent book. Happily, it was not so. Combinatorics Ancient and … Continue reading
Posted in books
Tagged block designs, graph theory, history of mathematics, Latin squares, partitions
1 Comment