Upcoming Seminars

MONDAY, December 3, 2007

        APPLIED ANALYSIS AND PDE READING SEMINAR     PSA 304   1:40 p.m.
        Moderators: Slim Ibrahim, Svetlana Roudenko, Sergei Suslov,
                    Department of Mathematics and Statistics
          "Local and Global Analysis of Nonlinear Dispersive Equations"
        ABSTRACT: We study in details modern approaches in Analysis and
        Nonlinear PDEs based on the book from CBMS series by Terence
        Tao (Field's Medalist 2006). Graduate students and postdocs are
        especially welcome.

WEDNESDAY, December 5, 2007

        COMBINATORICS SEMINAR                        PSA 206   4:00 p.m.
        Einar Steingrimsson, Reykjavik University, Iceland
          "Stack Sorting, Trees and Pattern Avoidance"
        ABSTRACT: The subject of pattern avoiding permutations has its
        roots in computer science, namely in the problem of sorting a
        permutation through a stack.  A formula for the number of
        permutations of length N that can be sorted by passing it twice
        through a stack (where the letters on the stack have to be in
        increasing order) was conjectured by Julian West, and later
        proved by Doron Zeilberger. Goulden and West found a bijection
        from such permutations to rooted nonseparable planar maps, and
        later Cori, Jacquard and Schaeffer presented a bijection from
        these planar maps to certain labeled plane trees.
          We show that these labeled plane trees are in one-to-one
        correspondence with permutations that avoid the generalized
        patterns 3-1-4-2 and 2-41-3. We do this by establishing a
        bijection, which preserves 7 statistics, between the avoiders
        and the trees. This also gives rise to a seemingly new
        involution on (unlabeled) plane trees with interesting
        properties.
          This is joint work (in progress) with Anders Claesson and
        Sergey Kitaev.