Math Colloquium

### Speaker: Anders Claesson

Title: Interval orders via combinatorial species and ballot matrices

Location: V-157, VRII.

Time: Friday, Februar 5 at 13:20.

### Abstract:

We give a brief introduction to (some aspects of) combinatorial species.

Using this framework we introduce ballot matrices and present a subset

of them that is in bijection with labeled interval orders. Such ballot

matrices decompose naturally into a pair of permutations with related

properties, which leads to a new formula for the number of labeled

interval orders.

This talk is based on joint work with Stuart Hannah.

Math Colloquium

### Speaker: Bjarni Jens Kristinsson, University of Iceland, and Henning Úlfarsson, Reykjavik University

Title: Occurrence graphs of patterns in permutations

Location: Naustið, Endurmenntun (here)

Time: Thursday, June 04, at 15:00-16:00.

### Abstract:

This paper is based on a generalisation of the idea behind the proof of the Simultaneous Shading Lemma by Claesson et al. (2014). We define the occurrence graph \(G_p(\pi)\) of a pattern \(p\) in a permutation \(\pi\) as the graph with the occurrences of \(p\) in \(\pi\) as vertices and edges between the vertices if the occurrences differ by exactly one element. We study the general properties of the occurrence graphs and some interesting extreme cases. The main theorem in this paper is that every hereditary property of graphs produces a permutation class.

Math Colloquium

### Speaker: Henning Ulfarsson, Reykjavik University

Title: Struct: An algorithm for guessing the structure and enumeration of permutation sets

Location: Naustið, Endurmenntun (here)

Time: Tuesday January 22.,15:00-16:00.

### Authors:

Michael Albert, Anders Claesson, Bjarki Gudmundsson, Henning Ulfarsson

### Abstract:

Struct is an algorithm being developed by the authors to

guess the structure of a set of permutations. In some cases the structure

discovered is sufficient to infer the generating function of the set and

provides an enumeration of the permutations by length. A preliminary version of

the algorithm will be presented and applied to several sets of permutations.

This research is funded by the Icelandic Research Fund, Grant no.~141761-051