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Graduate Seminar
Emily Allen Carnegie Mellon University Title: SuperCatalan Numbers Abstract: The Catalan numbers are a well known sequence of integers that arise in many combinatorial problems. They have multiple qanalog polynomials, one of which is the generating function for the major index of Catalan Paths. The superCatalan 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 qanalog polynomial of the superCatalan 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 