Conference Agenda

Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).

 
Session Overview
Session
MS137, part 1: Symbolic Combinatorics
Time:
Thursday, 11/Jul/2019:
10:00am - 12:00pm

Location: Unitobler, F005
53 seats, 74m^2

Presentations
10:00am - 12:00pm

Symbolic Combinatorics

Chair(s): Shaoshi Chen (Chinese Academy of Sciences), Manuel Kauers (Johannes Kepler University, Linz, Austria), Stephen Melczer (University of Pennsylvania)

In recent years algorithms and software have been developed that allow researchers to discover and verify combinatorial identities as well as understand analytic and algebraic properties of generating functions. The interaction of combinatorics and symbolic computation has had a beneficial impact on both fields. This minisymposium will feature 12 speakers describing recent research combining these areas.

 

(25 minutes for each presentation, including questions, followed by a 5-minute break; in case of x<4 talks, the first x slots are used unless indicated otherwise)

 

Enumeration of walks in three quarters of the plane

Axel Bacher
University Paris 13

Walks in the quarter plane with a prescribed set of steps have, in the past decades, attracted a lot of attention. One of the main question is to find the nature of the generating function (algebraicity, D-finiteness, etc.) as a function of the step set. Since these walks are now rather well understood, we turn our attention to a related problem, walks in three quarters of the plane, for which we present the latest results.

Work in common with Alin Bostan and Killian Raschel.

 

On the growth of algebras

Jason Bell
University of Waterloo

The growth function of an algebra is a combinatorial invariant that gives insight into the underlying algebraic structure. There are several well-known combinatorial constraints that growth functions must have. We show that in fact all constraints are now known: given a function satisfying the previously known constraints, we show that there is an algebra having this function as its growth function. This is joint work with Efim Zelmanov.

 

A Gessel way to the diagonal theorem on D-finite power series

Shaoshi Chen
Chinese Academy of Sciences

Special functions that satisfy linear differential equations with polynomial coefficients appear ubiquitously in combinatorics and mathematical physics. Such special functions are said to be D-finite by Stanley. In the early 1980's, Gessel and Zeilberger independently proved that the diagonal of D-finite power series in several variables is D-finite. However their proofs were not complete and later Lipshitz gave a complete proof using an elimination lemma. Zeilberger completed his proof with the theory of holonomic D-modules. We follow the spirit of Gessel's proof strategy and fix the gap in his proof directly. This is a joint work with Chaochao Zhu.

 

Inhomogeneous Lattice Walks

Manfred Buchacher
Johannes Kepler University Linz

We consider inhomogeneous lattice walk models in a half-space and in the quarter plane. For the models in a half-space, we show by a generalization of the kernel method to linear systems of functional equations that their generating functions are always algebraic. For the models in the quarter plane, we have carried out an experimental classification of all models with small steps. We discovered many (apparently) D-finite cases for most of which we have no explanation yet.

Joint work with Manuel Kauers. To appear in the proceedings of FPSAC 2019.