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A214396 Number of HSI-algebras on n elements, up to isomorphism. 0
1, 5, 44 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

An HSI-algebra is a structure (1, +, *, ^) over some set such that Tarski's high-school identities hold: addition and multiplication are commutative and associative, multiplication distributes over addition, 1 is the multiplicative identity, x^1 = x, 1^x = 1, x^y * x^z = x^(y+z), (xy)^z = x^z * y^z, and (x^y)^z = x^(y*z).

Burris & Lee (1992) find a(3) = 44.

LINKS

Table of n, a(n) for n=1..3.

S. Burris and S. Lee, Small models of the high school identities, International Journal of Algebra and Computation 2:2 (1992), pp. 139-178.

S. Burris and S. Lee, Tarski's high school identities, Amer. Math. Monthly 100 (1993), 231-236.

FORMULA

Trivial upper bound: a(n) <= n^(3n^2+1). - Charles R Greathouse IV, Jun 19 2013

CROSSREFS

Cf. A007459.

Sequence in context: A079646 A292697 A098891 * A247712 A030698 A080284

Adjacent sequences:  A214393 A214394 A214395 * A214397 A214398 A214399

KEYWORD

nonn,nice,hard,more,bref

AUTHOR

Charles R Greathouse IV, Aug 21 2012

STATUS

approved

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Last modified August 24 18:12 EDT 2019. Contains 326295 sequences. (Running on oeis4.)