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A358471 a(n) is the number of transitive generalized signotopes.

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%I A358471 #23 Dec 25 2022 20:25:28
%S A358471 2,14,424,58264,33398288,68779723376
%N A358471 a(n) is the number of transitive generalized signotopes.
%C A358471 A "transitive generalized signotope" is a generalized signotope X (cf. A328377) with the additional property that for any 5-tuple p, q, r, s, t, if (X(t,q,r), X(p,t,r), X(p,q,t), X(s,q,t), X(p,s,t), X(p,q,s)) = (+,+,+,+,+,+), then X(s,q,r)=+. Here X is extended to non-ordered triples by X(p(a),p(b),p(c)) = sgn(p)X(a,b,c) for any permutation p of three elements.
%C A358471 The "transitivity property" from the definition has a nice interpretation in the context of point sets, see "transitive interior triple systems" in Knuth.
%C A358471 The condition of transitivity from the definition above is implication (2.4a) in Knuth.
%C A358471 Every signotope (cf. A006247) is a transitive generalized signotope, giving a lower bound of 2^(c*n^2) <= a(n). This can be seen by checking the n=5 case. A violating 5-tuple in any signotope then cannot occur because it induces a signotope on 5 elements.
%D A358471 D. Knuth, Axioms and Hulls, Springer, 1992, 9-11.
%Y A358471 Cf. A006247, A328377.
%K A358471 nonn,more
%O A358471 3,1
%A A358471 _Robert Lauff_, Nov 18 2022