**Copyright © by**

**Lehrstuhl II für Mathematik**

**Department of Mathematics**

**University of Bayreuth**

**Postfach 10 12 51**

**8580 Bayreuth, Germany**

This program system is devoted to the linear representation theory, the invariant theory and the combinatorics of finite symmetric groups and related classes of groups. It was developed jointly at the Lehrstühle II/IV für Mathematik, University of Bayreuth, at the LITP, Université Paris VII, and at the University of Wales, Aberystwyth. Financial support by the Deutsche Forschungsgemeinschaft and the European exchange programs PROCOPE and ARC is gratefully acknowledged.

The permission to redistribute this software remains at the Lehrstuhl II für Mathematik. Copies are distributed freely for non-commercial purposes only. You will get the program source together with a LaTeX-source for this introductory user's guide.

SYMMETRICA is distributed without any warranty. Please inform us about bugs, modifications, wishes, improvements and applications.

- Preface
- The installation
- The use of SYMMETRICA
- More details
- Mixed examples
- Combinatorics
- Symmetric polynomials
- Multivariate polynomials
- Finite group actions
- Orbit-enumeration in SYMMETRICA
- Some basic cycle index formulae
- Multi-dimensional cycle indices
- The cycle indices of the symmetry groups of platonic solids
- Linear, affine and projective groups
- Induced cycle indices
- Products of cycle indices
- The Redfield operators
- Substitutions into cycle indices
- Some further cycle index routines
- Some example programs

- Orbit-construction in SYMMETRICA
- Applications

- Orbit-enumeration in SYMMETRICA
- Characters
- Plethysms
- Matrix representations
- Symmetry adapted bases
- The arithmetic

- The Objects
- Index
- References
- Footnotes

harald.fripertinger "at" uni-graz.at, May 26, 2011