cp's OEIS Frontend

A367445 Number of discrete implications I:L_n^2-> L_n defined on the finite chain L_n={0,1,...n}, which satisfy the contrapositive symmetry with respect to some discrete negation N, i.e., I(x,y) = I(N(y), N(x)), for all x,y in L_n.

%I A367445 #5 Nov 19 2023 10:33:58
%S A367445 1,8,99,2828,152474
%N A367445 Number of discrete implications I:L_n^2-> L_n defined on the finite chain L_n={0,1,...n}, which satisfy the contrapositive symmetry with respect to some discrete negation N, i.e., I(x,y) = I(N(y), N(x)), for all x,y in L_n.
%C A367445 Number of discrete implications I:L_n^2-> L_n defined on the finite chain L_n={0,1,...n} satisfying the contrapositive symmetry with respect to some discrete negation N, i.e., the number of binary functions I:L_n^2->L_n such that I is decreasing in the first argument, increasing in the second argument, I(0,0)=I(n,n)=n and I(n,0)=0 (discrete implication), and I(x,y) = I(N(y), N(x)), for all x,y in L_n (contrapositive symmetry with respect to a discrete negation N). A discrete negation N:L_n->L_n is a decreasing operator with N(0)=n and N(n)=0.
%H A367445 M. Munar, S. Massanet and D. Ruiz-Aguilera, <a href="https://doi.org/10.1016/j.fss.2023.01.004">A review on logical connectives defined on finite chains</a>, Fuzzy Sets and Systems, Volume 462, 2023.
%Y A367445 Particular case of the enumeration of discrete implications in general, enumerated in A360612.
%Y A367445 The enumeration of discrete negations in general is given in A001700.
%Y A367445 When the discrete negation is N(x)=n-x, for all x in L_n, the enumeration is given in A366540.
%K A367445 nonn,hard,more
%O A367445 1,2
%A A367445 _Marc Munar_, Nov 18 2023