|Date: Friday, February 24, 2012
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: Maximal crossing and nesting of random matchings
Abstract: The number of complete matchings on [2n] with no crossings equals the Catalan number and so does the number of matchings with no nestings. The notion of r-crossing (r-nesting) matchings is a generalization of matchings with no crossings (nestings). The number of matchings with no j-crossing and no k-nesting was evaluated by Chen, Deng, Du, Stanley and Yan in 2007 in terms of a Toeplitz determinant. This work was based on a bijection between partitions and vacillating tableaux. Building on their work, we study the limiting joint distribution of the maximal crossing and the maximal nesting of random Poissonized matchings. This is a joint work with Robert Jenkins (UM).
Speaker: Jinho Baik
Institution: University of Michigan