A001427 Number of regular semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
1, 3, 9, 42, 206, 1352, 10168, 91073, 925044
Offset: 1
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
- 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.
- 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
- 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, Semigroup Forum, 14 (1977), 69-79.
- 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)
- S. Satoh, K. Yama, M. Tokizawa, Semigroups of order 8, Semigroup Forum 49 (1994), 7-29.
- 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
Extensions
a(8) and a(9) from Andreas Distler, Jan 17 2011