Mathematics Colloquia and Seminars
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Refined enumeration of pattern-avoiding permutationsAlgebra & Discrete Mathematics
|Speaker: ||Sergi Elizalde, MSRI|
|Location: ||693 Kerr|
|Start time: ||Fri, Oct 1 2004, 12:10PM|
The talk will begin with a short survey of some of the main enumerative
results in the subject of restricted (or pattern-avoiding) permutations.
Next I will discuss some recent work concerning statistics on restricted
permutations, motivated in part by the surprising result of Zeilberger et
al. which states that the number of fixed points has the same distribution
in 321-avoiding permutations as in 132-avoiding permutations. I will give
two combinatorial proofs of this result, and generalize it to other
statistics. Bijections to Dyck paths play an important role in the proofs.
Finally I will consider permutations avoiding several patterns
simultaneously, as well as generalized patterns (i.e., with the
requirement that some elements occur in adjacent positions). Using similar
bijections we obtain generating functions enumerating these restricted
permutations with respect to several statistics.
join us for lunch at 1pm; dinner at (?) 6pm.