A001427 Number of regular semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator). (Formerly M2823 N1136)

1, 3, 9, 42, 206, 1352, 10168, 91073, 925044

Offset

1,2

References

Tak-Shing T. Chan, YH Yang, Polar n-Complex and n-Bicomplex Singular Value Decomposition and Principal Component Pursuit, IEEE Transactions on Signal Processing ( Volume: 64, Issue: 24, Dec.15, 15 2016 ); DOI: 10.1109/TSP.2016.2612171

H. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, Semigroup Forum, 14 (1977), 69-79.

R. J. Plemmons, There are 15973 semigroups of order 6, Math. Algor., 2 (1967), 2-17; 3 (1968), 23.

R. J. Plemmons, Cayley Tables for All Semigroups of Order Less Than 7. Department of Mathematics, Auburn Univ., 1965.

S. Satoh, K. Yama, M. Tokizawa, Semigroups of order 8, Semigroup Forum 49 (1994), 7-29.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..9.

Andreas Distler, Classification and Enumeration of Finite Semigroups, A Thesis Submitted for the Degree of PhD, University of St Andrews (2010).

H. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, annotated and scanned copy.

R. J. Plemmons, There are 15973 semigroups of order 6 (annotated and scanned copy)

N. J. A. Sloane, Overview of A001329, A001423-A001428, A258719, A258720.

T. Tamura, Some contributions of computation to semigroups and groupoids, pp. 229-261 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970. (Annotated and scanned copy)

Index entries for sequences related to semigroups

Crossrefs

Sequence in context: A057724 A129879 A264521 * A020128 A018995 A018965

Adjacent sequences: A001424 A001425 A001426 * A001428 A001429 A001430

Keyword

nonn,nice,hard,more

Author

N. J. A. Sloane

Extensions

a(8) and a(9) from Andreas Distler, Jan 17 2011

Status

approved