Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
Title: 321-avoiding permutations
Speaker: Vince Vatter, University of Florida
Date: Thursday, March 7, 2013 5:00pm
Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ
It is well-known that the 321-avoiding permutations are counted by the Catalan numbers, and thus have an algebraic generating function. I will prove that every subclass of the 321-avoiding permutations which is defined by only finitely many additional restrictions has a rational generating function. The primary proof technique is the theory of formal languages applied to a restricted version of the ``staircase decomposition'' which every 321-avoiding permutation possesses. This is joint work with Michael Albert and Nik Ruskuc.