Tables

Abstract

This chapter contains tables of marks and Burnside matrices of the smallest cyclic, dihedral, symmetric and alternating groups. Moreover, the interested reader will find characters (reducible and irreducible) of symmetric groups, in order to support further applications by providing some numerical information. The irreducible char­acters are given, together with the Young characters and their decompositions. Also the scalar products of Young characters and products of Young characters and the al­ternating character are tabulated, since these numbers are numbers of 0–1-matrices with prescribed row and column sums. In addition the smallest Foulkes tables are shown since the characters occuring in enumeration theory of symmetry classes of mappings are linear combinations of Foulkes characters. Then the first 44 character polynomials are listed, each of them allows to evaluate an infinite series of ordinary irreducible characters of symmetric groups. The final section contains the 120 first Schubert polynomials.