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# Tag Archives: Latin squares

## The Hall–Paige conjecture

A Latin square of ordern is an n×n array of symbols from an alphabet of size n with the property that each symbol in the alphabet occurs once in each row or column. Two Latin squares L and M are … Continue reading

## British Mathematical Colloquium, days 3 and 4

The day began with the plenary talk by Paul Seymour, whom I’ve known for longer than almost anyone else at the meeting. He explained that there are many different “ordering” relations on graphs; the two he considers most important are … Continue reading

## Equitable partitions of Latin square graphs

On our recent trip to Shanghai, Rosemary Bailey and I met Sergey Goryainov, who gave a talk about some joint work with his supervisor Alexander Gavrilyuk at the International Workshop on Bannai–Ito Theory in Hangzhou. I mentioned it in my … Continue reading

Posted in Uncategorized
Tagged eigenvalue, equitable partition, Latin squares, quotient matrix, strongly regular graphs
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## ACCMCC, Days 4 and 5

Penny Haxell opened proceedings on Thursday with her astonishing work with Ron Aharoni. They give a sufficient condition for a tripartite 3-uniform hypergraph (one whose vertex set is partitioned into three parts so that each hyperedge contains one vertex from … Continue reading

Posted in events
Tagged affine planes, Latin squares, Markov chains, switching, synchronization, transversals, Tutte polynomial
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## From the archive, 9

Looking for a book yesterday, I turned up a file of old papers. One of them I think deserves an afterlife, so I re-typed it and here it is. First, the background. Let A be an n×n matrix. The permanent … Continue reading

## 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, On-line Encyclopedia of Integer Sequences, parking functions, partitions, root systems, statistics, Sudoku, synchronization, Tehran
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## Orbital combinatorics

Yesterday I went to Edinburgh to give a colloquium talk about synchronization, including the recent stuff about butterflies. The day before, I had discussed Artur Schäfer’s work with him, and he expressed a hope that if he went to the … Continue reading

## A niggling problem

Preparing my talk for the Research Day, I was reminded of a problem I can’t solve, that has niggled me for many years. Maybe someone else can solve it, or maybe I will be encouraged to do it myself. Here … Continue reading

Posted in open problems
Tagged almost all quasigroups, Latin squares, loops, multiplication groups, quasigroups
3 Comments

## Futoshiki squares

Futoshiki is a puzzle in the spirit of sudoku, involving constructing a Latin square from some partial information, which can be found in some newspapers now, including the Saturday Guardian. Probably someone has looked at the mathematics of futoshiki, but … Continue reading

## 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