Algorithmic Combinatorics Seminar, Summer 2001

Time: every Friday, 10:00 - 12:00

Place: Seminarraum Schloß Hagenberg

09.03. Peter Paule Organizational items
Christian Weixlbaumer Notes on diploma thesis
16.03. Peter Paule Plane partition diamonds (SLC test run)
Axel Riese A computer proof of Kirkman's hypothesis
Axel Riese qMultiSum (SLC test run)
23.03. Cleo Pau (Gemeindesaal) Progress report (Part II)
30.03. Cleo Pau Progress report (Part III)
Burki Zimmermann Rogers-Ramanujan-Buchberger
06.04. canceled
27.04. Stefan Gerhold Uncoupling of linear Ore operator equations (Part I)
04.05. Stefan Gerhold Uncoupling of linear Ore operator equations (Part II)
Fabrizio Caruso C++/Mathematica Polynomial Library

Abstract: I will describe my C++/Mathematica Polynomial Library and some of the algorithms implemented in it: Newton Iteration for division and Division by Powers of Binomials "by Ansatz".

Florian Bachinger Proper Hypergeometric = Holonomic (Part I)
11.05. Florian Bachinger Proper Hypergeometric = Holonomic (Part II)
18.05. Rainer Nobis Representations of Numbers
25.05. Raimundas Vidunas (11:00) Identities with non-terminating hypergeometric series
01.06. canceled
08.06. Clemens Pechstein MacMahon's Partition Analysis
11.06. Temur Kutsia (15:00) Unification in the Empty and Flat Theories with Sequence Variables and Flexible Arity Symbols

Abstract: We define equational theory with sequence variables and flexible arity symbols and consider a general unification problem in two such theories: empty theory and flat theory (theory with a flat flexible arity symbol). We build terms over two types of variables - individual and sequence variables, object constants and two types of function symbols - of fixed and flexible arity. For sequence variables one can substitute any (possibly empty) sequence of terms. Presence of fixed arity symbols and sequence variables makes it necessary to solve a system of linear Diophantine equations over naturals in order to decide whether an expression of the theory is a term (or an equation) of the theory. We prove that unifiability in both theories is decidable and describe unification procedures, which enumerate the minimal and complete set of solutions of the problem and terminate, if the set is finite. The procedure for the empty theory is implemented on Mathematica and uses the Omega package to solve linear Diophantine equations.

15.06. canceled
21.06. Christian Krattenthaler (11:00) On plane partitions and alternating sign matrices

Abstract: I will give a survey on the enumeration of plane partitions and alternating sign matrices, a subject that has been, and still is, one of the most fascinating in enumerative and algebraic combinatorics. I will describe the most interesting methods that are used, and will conclude with some of the open problems and conjectures in the field.

22.06. Christian Neumaier On magic squares
25.06. Helmut Prodinger (13:30) Mathematical analysis of algorithms for broadcast communication
29.06. Martin Semrad On a conjecture of Borwein et al.