cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A076017 Number of nonisomorphic systems with n elements with one binary operation satisfying the equation B(AB)=A (semisymmetric quasigroups).

This page as a plain text file.
%I A076017 #27 Dec 09 2021 00:47:44
%S A076017 1,1,2,3,4,9,41,595,26620,3908953,1867918845
%N A076017 Number of nonisomorphic systems with n elements with one binary operation satisfying the equation B(AB)=A (semisymmetric quasigroups).
%C A076017 In January of 1968, _Don Knuth_ described the concept of what he called an "abstract grope" to the students in his class for sophomore math majors at Caltech.
%C A076017 The students had just learned about abstract groups and he wanted them to get experience doing research with other algebraic axioms; so he challenged them to prove as many interesting things as they could about sets of elements with a binary operator that satisfies the identity x(yx)=y.
%C A076017 The name came from the fact that they were groping for results. Such systems were studied in a series of papers by Sade under a more complicated and more dignified yet less memorable name, "semisymmetric quasigroups". The students came up with some good stuff, including the concept of normal subgropes.
%D A076017 D. E. Knuth, The Art of Computer Programming, Vol. 4B, in preparation.
%D A076017 A. Sade, Quasigroupes demi-symétriques, Ann. Soc. Sci. Bruxelles Sér. I 79 (1965), 133-143.
%H A076017 Brendan D. McKay and Ian M. Wanless, <a href="https://doi.org/10.1002/jcd.21814">Enumeration of Latin squares with conjugate symmetry</a>, J. Combin. Des. 30 (2022), 105-130.
%Y A076017 Cf. A076016-A076021.
%K A076017 nonn,hard,more
%O A076017 1,3
%A A076017 Richard C. Schroeppel, Oct 29 2002
%E A076017 a(10), a(11) and comments from _Don Knuth_, May 12 2005 - May 14 2005