login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A215651 Number of transformation semigroups acting on n points (counting conjugates as one), i.e., the number of subsemigroups of the full transformation semigroup T_n. 0
1, 2, 8, 283 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The semigroup analog of A000638.

We apply the categorical viewpoint and consider the empty set as a semigroup.

The fifth term has been calculated: 132069776. Currently, the result is being verified and the related publication is being prepared. - Attila Egri-Nagy, Jan 09 2014

LINKS

Table of n, a(n) for n=0..3.

PROG

(GAP)

################################################################################

# GAP 4.5 function calculating the conjugacy classes of a set of subsemigrops.

# (C) 2012 Attila Egri-Nagy www.egri-nagy.hu

# GAP can be obtained from www.gap-system.org

################################################################################

# Input: list of subsemigroups of a transformation semigroup,

#        automorphism group of the semigroup

# Output: list of conjugacy classes

ConjugacyClassesSubsemigroups := function(subsemigroups, G)

local ssg, #subsemigroup

      ccl, #conjugacy class

      ccls; #result: all conjugacy classes

  ccls := [];

  for ssg in subsemigroups do

    #we check whether the subsemigroup is already in a conjugacy class

    if not ForAny(ccls, x -> ssg in x) then

      #conjugating by all group elements

      ccl := DuplicateFreeList(

                     List(G,

                          g -> AsSortedList(List(ssg, t-> t^g))));

      Add(ccls, ccl);

    fi;

  od;

  return ccls;

end;

CROSSREFS

Cf. A215650.

Sequence in context: A012296 A009675 A012301 * A285850 A009501 A013027

Adjacent sequences:  A215648 A215649 A215650 * A215652 A215653 A215654

KEYWORD

nonn,more

AUTHOR

Attila Egri-Nagy, Aug 19 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified September 22 00:25 EDT 2017. Contains 292326 sequences.