A367444 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.

1, 10, 165, 3863, 117096

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 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).

Links

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

M. Munar, S. Massanet and D. Ruiz-Aguilera, On the cardinality of some families of discrete connectives, Information Sciences, Volume 621, 2023, 708-728.

M. Nachtegael and E. Kerre, Fuzzy logical operators on finite chains, International Journal of General Systems, Volume 29, 2000, 29-52.

Crossrefs

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

Sequence in context: A278096 A272499 A305604 * A054688 A229228 A112650

Adjacent sequences: A367441 A367442 A367443 * A367445 A367446 A367447

Keyword

nonn,hard,more

Author

Marc Munar, Nov 18 2023

Status

approved