SFB-Colloquium

Program:

14:00-14:20 Valerie Roitner (TU Wien): The average number of contacts in 2-watermelons without wall

Abstract:

This talk deals with 2-watermelons, i.e. a pair of nonintersecting Dyck-paths (with conditions on the start- and endpoints).

I will analyze the average number of contacts (i.e. the points where the path are at minimal distance from each other) in 2-watermelons and give both exact and asymptotic results for expected value and variance via a bijection with weighted Motzkin-paths.

14:20-14:40: Katarzyna Grygiel (TU Wien): Lambda terms, and what brought me to Vienna

Abstract:

Not as intriguingly as did Robert Graves with the story of Claudius, yet doing my best, I will briefly present myself, providing some insights into my interests and reasons that lead me to where I am now. And most importantly there will be several interesting connections between combinatorics and lambda calculus.

14:40-15:00: Ali Uncu (RISC, Hagenberg): Polynomial Identities that Imply Capparelli's Partition Theorems, and more

15:00-15:30: coffee break

15:30-16:15: Gaurav Bhatnagar (Universität Wien): Orthogonal polynomials associated with a continued fraction of Hirschhorn

Abstract:

We study orthogonal polynomials associated with a continued fraction due to Hirschhorn.

Hirschhorn's continued fraction contains as special cases  the famous Rogers--Ramanujan continued fraction and two of Ramanujan's generalizations.

The orthogonality measure of the set of polynomials obtained has an absolutely continuous component. We find generating functions, asymptotic formulas, orthogonality relations, and the Stieltjes transform of the measure. Using standard generating function techniques, we show how to obtain formulas for the convergents of Ramanujan's continued fractions, including a formula that Ramanujan recorded himself as Entry 16 in Chapter

16 of his second notebook. This is joint work with Mourad Ismail.