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Tag Archives: transversals
BCC29 at Lancaster
Last week we celebrated the 29th British Combinatorial Conference in Lancaster, face to face. (As a side observation, this was by far the largest social gathering I have been at since the start of the pandemic; I found it both … Continue reading
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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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 3uniform 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
1 Comment
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
Subsets and partitions
There are several packing and covering problems for subsets of a set, which have been worked over by many people. For example, given t, k and n, how many ksubsets of an nset can we pack so that no tsubset … Continue reading
Posted in mathematics, open problems
Tagged primitivity, sections, semigroups, transversals
1 Comment
Diamond squares
If you like Latin squares and such things, take a look at Diamond Geezer’s post for today: a pair of orthogonal Latin squares with two disjoint common transversals, and some entries given (if you do the harder puzzle).