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ICE-TCS Lectures Series - Henning Úlfarsson - Equivalence relations on permutations and pattern avoidance

Henning

The next ICE-TCS  talk for this semester will be delivered on Friday, 16 April,  by Henning Ulfarsson (Reykjavik University).  The talk, which is entitled Equivalence relations on permutations and pattern avoidance, will be held at 14:00 in room M1.05 at the new premises of Reykjavik University in Nauthólsvík.



Abstract

Usually when one studies pattern avoidance of permutations one fixes a particular pattern and counts the permutations that avoid the pattern. In this talk we will study the same counting problem when permutations are placed into equivalence classes with respect to some relation. Then the sizes of the classes that entirely avoid a pattern are added up. This leads to some new and interesting counts.

Three particular relations will be discussed, conjugacy, k-type and toric equivalence. The first one allows one to identify the permutations that do not contain a cycle of a prescribed length; the second one seems to give connections to palindromic words; and the last one gives some surprising connections with number theory.