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A027851 Number of nonisomorphic semigroups of order n. 25
1, 1, 5, 24, 188, 1915, 28634, 1627672, 3684030417, 105978177936292 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Peter Cameron's Blog, The combinatorial explosion, Posted 18/02/2016.
Andreas Distler, Classification and Enumeration of Finite Semigroups, A Thesis Submitted for the Degree of PhD, University of St Andrews (2010).
A. Distler and T. Kelsey, The semigroups of order 9 and their automorphism groups, arXiv preprint arXiv:1301.6023 [math.CO], 2013.
C. Noebauer, Home page
Arman Shamsgovara, Enumerating, Cataloguing and Classifying All Quantales on up to Nine Elements, In: Glück, R., Santocanale, L., and Winter, M. (eds), Relational and Algebraic Methods in Computer Science (RAMiCS 2023) Lecture Notes in Computer Science, Springer, Cham, Vol. 13896.
Jeremy G. Sumner, Michael D. Woodhams, Lie-Markov models derived from finite semigroups, arXiv:1709.00520 [math.GR], 2017.
Michael Torpey, Semigroup congruences: computational techniques and theoretical applications, Ph.D. Thesis, University of St. Andrews (Scotland, 2019).
Eric Weisstein's World of Mathematics, Semigroup.
FORMULA
a(n) = A001423(n)*2 - A029851(n).
a(n) + A079173(n) = A001329(n).
CROSSREFS
Sequence in context: A009601 A009676 A192995 * A120765 A259355 A297664
KEYWORD
nonn,hard,nice
AUTHOR
Christian G. Bower, Dec 13 1997, updated Feb 19 2001
EXTENSIONS
a(8)-a(9) from Andreas Distler, Jan 13 2011
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)