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

Author

David Radcliffe, Dec 21 2018

Keywords

• nonn
• more

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

• 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).

Crossrefs

Cf. A019538, A254570.

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.