Volume
and Number of Integral Points in Rational Polyhedra
This webpage hosts papers and
softwares about the problem of computing the volume and the number of
integral points in rational polyhedra (and its applications to
representation theory).
- Volume computation for
polytopes and partition functions for classical root systems.
Authors: M. W. Baldoni, M. Beck, C. Cochet, M. Vergne.
Abstract: This
paper presents an algorithm to compute the value of the inverse Laplace
transforms of rational functions with poles on arrangements of
hyperplanes. As an application, we present an efficient computation of
the partition function for classical root systems.
Paper: ps (2,3
Mo), pdf
(500 ko).
Status of the paper:
submitted. Also available on the arXiv:math.CO/0504231.
Softwares: compressed
archive (60 ko) containing Maple worksheets.
- Vector Partition and
Representation Theory
Author: C. Cochet.
Abstract:
We apply some recent developments of Baldoni-Beck-Cochet-Vergne on
vector partition function, to Kostant's and Steinberg's formulae, for
classical Lie algebras $A_r$, $B_r$, $C_r$, $D_r$. We therefore get
efficient {\tt Maple} programs that compute for these Lie algebras: the
multiplicity of a weight in an irreducible finite-dimensional
representation; the decomposition coefficients of the tensor product of
two irreducible finite-dimensional representations. These programs can
also calculate associated Ehrhart quasipolynomials.
Paper: ps
(2,6 Mo), pdf
(500 ko).
Status of the paper:
accepted for the proceedings of the conference Formal Power Series and Algebraic
Combinatorics 2005 (June 20-25, Taormina, Italy), being reviewed.
Softwares: not yet
distributed.
- Counting Integer Flows in
Networks
Authors: M. W. Baldoni,
J. De Loera, M. Vergne.
Abstract:
This paper discusses new analytic algorithms and software for the
enumeration of all integer flows inside a network. Concrete
applications abound in graph theory \cite{Jaeger}, representation
theory \cite{kirillov}, and statistics \cite{persi}. Our methods
clearly surpass traditional exhaustive enumeration and other
algorithms and can even yield formulas when the input data
contains some parameters. These methods are based on the study of
rational functions with poles on arrangements of hyperplanes.
Paper: ps
(500 ko), pdf
(400 ko).
Status of the paper:
Found. Comput. Math. 4 (2004), no.3, 277-314.
Also available on the arXiv:math.CO/0303228.
Softwares: compressed
archive (12 ko) containing Maple worksheets.
- Title of the paper
Author:
Abstract:
Paper:
Status of the paper:
Softwares: