A322654 Number of binary operations on an n-set that satisfy (ab)c = (ac)b for all a,b,c.

1, 1, 10, 573, 136528, 115511945, 365045461056

Offset

0,3

Comments

Equivalently, these are operations for which the functions induced by right multiplication commute with one another. The operations of subtraction, division, and exponentiation satisfy this identity on appropriate domains.

Links

Table of n, a(n) for n=0..6.

J. Benaloh and M. de Mare, One-Way Accumulators: A Decentralized Alternative to Digital Signatures, in: Tor Helleseth, Advances in Cryptology — EUROCRYPT '93, Springer-Verlag Berlin Heidelberg, 1994, 274-285 (Link to PDF).

Formula

a(n) = Sum_{k=1..n} k!*Stirling2(n,k)*c(n,k), where c(n,k) is the number of sets of k distinct functions from {1..n} to itself that are mutually commutative.

Crossrefs

Cf. A019538, A254570.

Sequence in context: A035308 A327412 A212925 * A337342 A323532 A273032

Adjacent sequences: A322651 A322652 A322653 * A322655 A322656 A322657

Keyword

nonn,more

Author

David Radcliffe, Dec 21 2018

Status

approved