Presenter: David Pike, Memorial University of Newfoundland

A $\lambda$-fold triple system of order $v$ consists of a $v$-set $V$ and a collection of 3-subsets (called blocks or triples) of $V$ such that each 2-subset of $V$ occurs in exactly $\lambda$ of the system's triples. Given a $\lambda$-fold triple system with $\lambda > 1$, we can ask whether its triples can be ordered so that the union of any two consecutive triples consists of four elements of $V$. We will describe

some potential applications, briefly review previous results, and discuss some recent work concerning the nonexistence / existence of such

orderings, with emphasis on 2-fold triple systems. This is joint work with Aras Erzurumluo\u{g}lu.

### About Pure mathematics seminars

We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.

Seminars are usually held on Tuesdays from 3pm to 3.50pm.

Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.

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