Dear Professor Mitchell, Thank you for helping me to solve this problem.
Given a partition P of a finite set X, I have already checked the above mentioned function "EndomorphismsPartition([]). This function only gives us the semigroup consisting of those transformations on X that preserve/stabilize the partition P of finite set X. But, I have been looking for a GAP function that gives the semigroup consisting of those transformations on X whose image set contains at least one element from each block of the partition P of finite set X. Best regards, \-Shubh On Mon, Oct 28, 2019 at 3:56 PM James Mitchell <j...@st-andrews.ac.uk> wrote: > Dear Shubh, > > There is the function EndomorphismsPartition in the Semigroups package > which does what you want, I think. The documentation is here: > > https://gap-packages.github.io/Semigroups/doc/chap8.html#X85C1D4307D0F5FF7 > > Best wishes, > > James > > James Mitchell > Professor of Mathematics > j...@st-andrews.ac.uk > > > > > On 25 Oct 2019, at 05:08, Shubh Narayan Singh (Assistant Professor, > Mathematics) <sh...@cub.ac.in> wrote: > > > > Dear all, > > Let X be a nonempty finite set and let P be an arbitrary partition of X. > > Denote by T(X, P) the semigroup of transformations preserving partition > P. > > > > Can anybody tell me a GAP code, if any, to compute the size of the > > subsemigroup of T(X, P) consisting of those transformations whose image > > intersects every block of P. > > > > Thanks in advance for your assistance. > > > > -- > > > > Sincerely, > > *------------------------------------------* > > > > *Shubh N. Singh, Ph.D.Assistant Professor * > > > > *Department of MathematicsCentral University of South Bihar* > > > > *Gaya–824236 (Bihar), INDIA-----------------------------------------* > > *E-mail: sh...@cub.ac.in <sh...@cub.ac.in>* > > *Mob: +91- 8404934146* > > _______________________________________________ > > Forum mailing list > > Forum@gap-system.org > > https://mail.gap-system.org/mailman/listinfo/forum > > -- Sincerely, *------------------------------------------* *Shubh N. Singh, Ph.D.Assistant Professor * *Department of MathematicsCentral University of South Bihar* *Gaya–824236 (Bihar), INDIA-----------------------------------------* *E-mail: sh...@cub.ac.in <sh...@cub.ac.in>* *Mob: +91- 8404934146* _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
