[GAP Forum] Help to compute the size of a semigroup of partition-preserving transformations

[Shubh Narayan Singh (Assistant Professor, Mathematics)]

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 <jdm3 at 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
> jdm3 at st-andrews.ac.uk
>
>
>
> > On 25 Oct 2019, at 05:08, Shubh Narayan Singh (Assistant Professor,
> Mathematics) <shubh at 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: shubh at cub.ac.in <shubh at cub.ac.in>*
> > *Mob:   +91- 8404934146*
> > _______________________________________________
> > Forum mailing list
> > Forum at 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: shubh at cub.ac.in <shubh at cub.ac.in>*
*Mob:   +91- 8404934146*