Examples of Calculations by means of PERMS

Mathematica Notebooks

Here we present a collection of Mathematica Notebooks which contain examples of calculations by means of the Mathematica package PERMS.

I compressed the Notebooks by gzip. They can be decompressed by the command

gzip -d -N name.gz  .
 

Calculations by means of PERMS

• The orbits of the group of Rubik's cube
• An automorphism of S₆ that is not an inner automorphism
• The sum of all Young symmetrizers of standard tableaux of S₅
• Calculation of the normalizer of the dicyclic group T₈
• The left ideal that describes the symmetry of the Riemannian curvature tensor
• The left ideal that describes the symmetry of the 1. covariant derivative of the Riemannian curvature tensor
• Determination of the numbers of ideals for products of the Riemannian curvature tensor
• The plethysm [2] * [3,2,1]
• The plethysm [2] * [4,2]
• Properties of the symmetrizers of tensors S*S and A*A

Calculations by means of PERMS and Ricci

The following notebooks contain examples which were produced by a cooperation of PERMS and the Mathematica tensor package Ricci written by J. M. Lee.

• The symmetry class of the Riemannian curvature tensor
• The symmetry class of the first covariant derivative of the Riemannian curvature tensor

Combinatorial treatment of a normal form problem of vector analysis

The following notebooks deal with a normal form problem of the classical vector analysis. You can find details about this problem in the

• text of a talk

that I gave at the 46. Seminaire Lotharingien de Combinatoire, Lyon, 2001. A table of the results is given in my list of mathematical tables on my home page. The calculations are stored in the following notebooks:

• Normal form problem of vector analysis - 4 vectors
• Normal form problem of vector analysis - 5 vectors
• Normal form problem of vector analysis - 6 vectors
• Normal form problem of vector analysis - 7 vectors
• Normal form problem of vector analysis - 8 vectors
• Normal form problem of vector analysis - 9 vectors

Determination of the structure of algebraic curvature tensors by means of Young symmetrizers.

The following notebooks contain calculations which belong to the investigations of my paper [12].

• Symmetrization of S*S and A*A by means of the Young symmetrizer of the Riemann tensor
• Symmetry operators connected with algebraic curvature tensors

Generators of algebraic covariant derivative curvature tensors and Young symmetrizers
Short formulas for algebraic covariant derivative curvature tensors

The following archive of 55 notebooks contains calculations which belong to the investigations of my papers [15] and [16]. The archive is a WinZip archive which can be decompressed by means of WinZip or by the command "unzip dacurvnb.zip".

• Download dacurvnb.zip