Tag Archives: transversals

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 k-universal transversal property (k-ut for short) if, given … Continue reading

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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

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A cliff

The “combinatorial explosion” is a well-known 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 k-subsets and all … Continue reading

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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 k-subsets of an n-set can we pack so that no t-subset … Continue reading

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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).

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