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ICE-TCS: Counting Patterns: Equipopularity in Permutation Classes

  • 18.5.2015, 14:00 - 15:00

Speaker: Cheyne Homberger (University of Maryland, Baltimore County, USA)

Identifying trends within data is a major problem across the sciences, and the theory of permutation classes adds new tools to this investigation.  By viewing sets of points on a plane as permutations, we can use these techniques to describe and explore patterns.  Given a set of permutations, two patterns are said to be equipopular if they occur equally often within the set.  One can show that, in the set of all permutations of a given length, all patterns of a fixed size are equipopular.

In this talk we explore the following question: How does the absence of one pattern affect the number of occurrences of another? This question leads to several interesting and surprising identities, concerning both individual patterns and the number of equipopularity classes themselves.  We begin by focusing on the number of small patterns in small-pattern avoiding permutations, before building to our main result: the classification of popularity classes within the separable permutations.

This talk will be accessible to a wide audience, and will include plenty of pictures.


Date and time: Monday, 18 May 2015, at 2pm (Note the nonstandard day)

Place: Room M102 



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