%I #8 Nov 18 2023 10:55:25

%S 1,10,165,3863,117096

%N Number of discrete implications I:L_n^2-> L_n defined on the finite chain L_n={0,1,...n}, which satisfy the exchange principle, i.e., I(x, I(y,z)) = I(y, I(x,z)), for all x,y,z in L_n.

%C Number of discrete implications I:L_n^2-> L_n defined on the finite chain L_n={0,1,...n} satisfying the exchange principle, 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, I(y,z)) = I(y, I(x,z)), for all x,y,z in L_n (exchange principle).

%H M. Munar, S. Massanet and D. Ruiz-Aguilera, <a href="https://doi.org/10.1016/j.ins.2022.10.121">On the cardinality of some families of discrete connectives</a>, Information Sciences, Volume 621, 2023, 708-728.

%H M. Nachtegael and E. Kerre, <a href="https://doi.org/10.1080/03081070008960923">Fuzzy logical operators on finite chains</a>, International Journal of General Systems, Volume 29, 2000, 29-52.

%Y Particular case of the enumeration of discrete implications in general, enumerated in A360612.

%K nonn,hard,more

%O 1,2

%A _Marc Munar_, Nov 18 2023