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Graduate Seminar

Emily Allen
Carnegie Mellon University
Title: Super-Catalan Numbers

Abstract: The Catalan numbers are a well known sequence of integers that arise in many combinatorial problems. They have multiple q-analog polynomials, one of which is the generating function for the major index of Catalan Paths. The super-Catalan numbers, (2n)!(2m)!/[n!m!(n+m)!], have been of interest lately. While we have known since the early 1900's that they are indeed integers, a combinatorial interpretation is unknown for m > 2. We will give a weighted interpretation, in which some objects have negative weights, and discuss what is necessary to remove the negative weights. We will introduce a q-analog polynomial of the super-Catalan numbers and provide a new result: an interpretation of the coefficients of the polynomials for m=2.

Date: Wednesday, February 5, 2014
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Brian Kell