GAP Manual: 50.30. PermBounds

PermBounds( tbl )

All characters pi satisfying pi(g) > 0 and pi(1) = d for a given degree d lie in a simplex described by these conditions. PermBounds computes the boundary points of this simplex for d = 0, from which the boundary points for any other d are easily derived. Some conditions from the powermap are also involved.

For this purpose a matrix similar to the rationalized character table has to be inverted.

These boundary points are used by PermChars (see PermChars) to construct all permutation character candidates of a given degree. PermChars either calls PermBounds or takes this information from the record field bounds of its argument record.