Dear Forum, On Wed, May 31, 2006 at 04:01:09PM +0100, John McDermott wrote: > Dear Fernando, > > You sent your message below to an incorrect address - it was received > by moderators of the Forum mailing list. I have copied this reply to > the GAP Forum ([EMAIL PROTECTED]). > > Best wishes, > John. > > On 31 May 2006, at 15:50, Fernando Fantino wrote: > > >Is there a GAP command that tests whether two permutations have the > >same = > >cycle type structure? > > > >i.e. if x=(123) (45)(789) > > > >" command? " (x) = ( 3 , 2 , 2 ). > > > >Thanks. Fernando
To find the command for the cycle structure, he could try: gap> ?CycleStructure Help: several entries match this topic - type ?2 to get match [2] [1] Reference: CycleStructurePerm [2] Reference: CycleStructureClass gap> ?1 > CycleStructurePerm( <perm> ) A is the cycle structure (i.e. the numbers of cycles of different lengths) of <perm>. This is encoded in a list <l> in the following form: The <i>-th entry of <l> contains the number of cycles of <perm> of length <i+1>. If <perm> contains no cycles of length <i+1> it is not bound. Cycles of length 1 are ignored. gap> SignPerm((1,2,3)(4,5)); -1 gap> CycleStructurePerm((1,2,3)(4,5,9,7,8)); [ , 1,, 1 ] On the other hand, if the cycle structure is irrelevant and he just wants to check two permutations have the same cycle type structure as he asked, then he need only check conjugacy in the mutually enclosing symmetric group: gap> IsConjugate(SymmetricGroup(4), (1,2)(3,4), (1,3)(2,4)); true [Two permutations of S_n are conjugate in S_n iff they have the same cycle structure.] Regards, Greg Gamble _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
