A001427 - OEIS

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)

%I M2823 N1136 #31 Dec 19 2021 09:00:00

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

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

%D 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

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

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

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

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

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

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

%H Andreas Distler, <a href="http://hdl.handle.net/10023/945">Classification and Enumeration of Finite Semigroups</a>, A Thesis Submitted for the Degree of PhD, University of St Andrews (2010).

%H H. Juergensen and P. Wick, <a href="/A001423/a001423.pdf">Die Halbgruppen von Ordnungen <= 7</a>, annotated and scanned copy.

%H R. J. Plemmons, <a href="/A001423/a001423_2.pdf">There are 15973 semigroups of order 6</a> (annotated and scanned copy)

%H N. J. A. Sloane, <a href="/A001329/a001329.jpg">Overview of A001329, A001423-A001428, A258719, A258720.</a>

%H T. Tamura, <a href="/A001329/a001329.pdf">Some contributions of computation to semigroups and groupoids</a>, pp. 229-261 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970. (Annotated and scanned copy)

%H <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>

%K nonn,nice,hard,more

%O 1,2

%A _N. J. A. Sloane_

%E a(8) and a(9) from _Andreas Distler_, Jan 17 2011