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.

1, 8, 99, 2828, 152474

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..5.

M. Munar, S. Massanet and D. Ruiz-Aguilera, A review on logical connectives defined on finite chains, Fuzzy Sets and Systems, Volume 462, 2023.

Crossrefs

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

The enumeration of discrete negations in general is given in A001700.

When the discrete negation is N(x)=n-x, for all x in L_n, the enumeration is given in A366540.

Sequence in context: A305919 A286841 A356440 * A316870 A181034 A324067

Adjacent sequences: A367442 A367443 A367444 * A367446 A367447 A367448

Keyword

nonn,hard,more

Author

Marc Munar, Nov 18 2023

Status

approved