> < ^ Date: Tue, 11 May 1993 17:48:45 +0200
> < ^ From: Thomas Breuer <Thomas.Breuer@Math.RWTH-Aachen.DE >
< ^ Subject: Re: PermChars

Dear Mrs. and Mr. Forum,

Kay Magaard writes

Using the 3.1 version of GAP I noticed the following:

On the one hand I get:

gap> A:=CharTable("Symmetric",6);;
gap> PermChars(A,6);
[ ]
gap> PermChars(A);
Error, Variable: 'mino' must have a value at
for <var> in [ maxu .. mino ] ... in
suche( 2 ) called from
Permut( tbl, arec ) called from
PermChars( A ) called from
main loop
brk> quit;

On the other hand I get:

gap> A:=CharTable("S6");;
gap> PermChars(A,6);
[ [ 6, 2, 0, 3, 0, 1, 0, 4, 2, 0, 1 ],
  [ 6, 2, 3, 0, 0, 1, 4, 0, 2, 1, 0 ] ]

Does a generic character table need to be reordered before
asking for permutaion characters?
If so how?

As Kay suspected and Goetz Pfeiffer told in his message to the forum,
the reason for the error message and the incorrect answer in the case
of the generic table is that the trivial character is not the first
one in the list of irreducibles. Of course this is a bug (in fact there
are two bugs, since 'PermChars' calls different algorithms for the
calculation of all permutation character candidates or of all of a
prescribed degree), since according to the manual (section 'Conventions'),
no program shall expect the trivial character to be the first one.
These bugs will be fixed in the next upgrade. In the current version of
GAP, the user should move the trivial character to the first position when
using 'PermChars', as proposed by Goetz.

Kind regards

Thomas Breuer

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