# The Endomorphism Conjecture for Posets

## Combinatorics/Partitions Seminar

## Meeting Details

For more information about this meeting, contact Barbara Baum.

**Speaker:** Ryan Flynn, Department of Mathematics, The Pennsylvania State University

**Abstract:** Let P be a finite partially ordered set. An automorphism of P is an order-preserving bijection from P to P, and an endomorphism of P is an order preserving map from P to P. The set of automorphisms of P forms a group under composition, and is denoted Aut(P). The set of endomorphisms of P forms a monoid under composition, and is denoted End(P).
The Endomorphism conjecture states, roughly, that as the cardinality of P becomes large, the ratio #Aut(P)/#End(P) tends to 0. This problem is surprisingly hard! We prove the conjecture for join-semilattices, and if time permits, for posets that are 'wide enough'.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 04/28/2009

**Time:** 11:15am - 12:05pm