Dear all,
This week we have a talk by Archna Kumari of IIT, Delhi. Here is the announcement.
Talk Announcement:
Title: Some results in weighted and elliptic enumeration
Speaker: Archna Kumari (IIT, Delhi)
When: Mar 27, 2025, 4:00 PM- 5:00 PM IST (Our usual time)
When: Mar 27, 2025, 4:00 PM- 5:00 PM IST (Our usual time)
Where: Zoom: Write to sf and nt at gmail dot com for the link
Live LInk: https://youtube.com/live/6U6er9-X7ZE?feature=share
Abstract
In the literature, there are a lot of $q$-identities. In this talk, we will talk about two types of $q$-identities and their extension to the elliptic case. First, we extend some Fibonacci identities using combinatorial methods. Since many of these identities can be derived through telescoping, we use this technique to find elliptic versions of basic elementary identities, such as the sum of the first odd or even numbers, the geometric series sum, and the sum of the first cubes. Along the way, we discover a multi-parameter identity that seems to be new, even in the -setting. Second, we will extend some $q$-hypergeometric identities to elliptic hypergeometric. We derive four expansion formulas and, as a result, some transformation formulas. In the $ q$ case, when the nome $p=0$, one of the formulas generalizes the basic hypergeometric transformation formula due to Liu, and Wang and Ma. The remaining three are equivalent to the well-poised Bailey lemma. Thus, we recover transformation formulas from Warnaar and Spiridonov.
This is joint work with Gaurav Bhatnagar and Michael Schlosser.
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