On Sun, Mar 8, 2020 at 5:13 AM David Joyner <wdjoy...@gmail.com> wrote:
> > > On Sun, Mar 8, 2020 at 4:58 AM Samuel Lelièvre <samuel.lelie...@gmail.com> > wrote: > >> Dear sage-combinat-devel, >> >> Please share any insight on this question >> about the image of a permutation: >> >> https://groups.google.com/d/msg/sage-devel/kk1C8LrSOTU/8W1r7LIPAgAJ >> >> > I agree with Michael O, a permutation is a bijection, > so the image is the domain is the codomain. > For a patch to "define the image of a permutation > to be the set of elements that it does not fix" is a > mistake, IMHO. Maybe the set computed could be > called "moved_points" or something like that? > > On a tangential matter, I'd like to add that according to Dan Bump's notes "Group Representation Theory" (http://sporadic.stanford.edu/bump/group/gr1_4.html), this set of elements that the permutations does not fix is called the support. If that is true then the SageMath support does not seem to be implemented correctly: sage: G = SymmetricGroup(10) sage: g = G.random_element(); g (1,3,6,7,4)(5,8,9) sage: g.support() {1, 2, 3, 4, 5, 6, 7, 8} sage: g = G.random_element(); g (1,6)(2,8)(3,9,10)(5,7) sage: g.support() {1, 2, 3, 4, 5, 6, 7, 8, 9} This is in sage 9.0b3. > >> Kind regards, >> Samuel Lelièvre >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sage-combinat-devel" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to sage-combinat-devel+unsubscr...@googlegroups.com. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sage-combinat-devel/CAEcArF1rkKgNxh5AfZJzLcQj0FeYSS7j6tHSVHvjJtRMvzgYDg%40mail.gmail.com >> . >> > -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-combinat-devel/CAEQuuAVjoKsvdZrqoFdbCXZ%2BtknsgeDjiEkSKE5BZG8SMBqhwA%40mail.gmail.com.
