Refined enumeration of pattern-avoiding permutations.
Sergi Elizalde, (MIT)
Abstract: The talk will begin with a survey of some of the main enumerative
results in the subject of restricted (or pattern-avoiding)
permutations. Next, recent developments and new directions will be
discussed, including simultaneous avoidance of several patterns,
enumeration of occurrences of a particular pattern in
permutations, and generalized patterns (i.e., with the requirement
that some elements occur in adjacent positions). The second part
of the talk will focus on the study of statistics in restricted
permutations, in which bijections to Dyck paths play an important
role. We give a new bijection between 321-avoiding permutations
and 132-avoiding permutations that preserves the number of fixed
points and the number of excedances. We will discuss recent work
with Emeric Deutsch, Toufik Mansour, Marc Noy and Igor Pak.
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