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Integrable systems blackboard seminar
various ways to obtain a polynomial equation with one catalytic variable
various ways to obtain a polynomial equation with one catalytic variable
Organizers
Speaker
Time
Monday, December 1, 2025 3:20 PM - 4:30 PM
Venue
A7-201
Abstract
In combinatorial literatures, discrete difference equations are always called polynomial equation with one catalytic variable. Under some mild conditions, it is possible to find a unique formal series solution. The solving strategy was first proposed (concluded) in 2006 by MIREILLE BOUSQUET-MÉLOU and many problems was solved in this framework.
In this talks I would like to introduce three different ways to achieve a polynomial equation with one catalytic variable. The first is the kernel method, the second is Riemann boundary value problem with Carleman shift. The third is the Tutte invariant method. I will introduce the ideas without the giving full proofs. I pick examples from different literatures by MIREILLE BOUSQUET-MÉLOU, ANDREW ELVEY PRICE, Kilian Raschel and also my recent work. The examples incudes lattice walk in different domains and some graph enumeration problems.
In this talks I would like to introduce three different ways to achieve a polynomial equation with one catalytic variable. The first is the kernel method, the second is Riemann boundary value problem with Carleman shift. The third is the Tutte invariant method. I will introduce the ideas without the giving full proofs. I pick examples from different literatures by MIREILLE BOUSQUET-MÉLOU, ANDREW ELVEY PRICE, Kilian Raschel and also my recent work. The examples incudes lattice walk in different domains and some graph enumeration problems.