COUNTING FINITE ALGEBRAS IN THE POST VARIETIES-Reference-Cited by-同舟云学术

COUNTING FINITE ALGEBRAS IN THE POST VARIETIES

Published:2000-06 Issue:03 Volume:10 Page:323-337
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

BERMAN JOEL¹,IDZIAK PAWEŁ²

Affiliation:

1. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, USA

2. Computer Science Department, Jagiellonian University, Kraków, Poland

Abstract

The G -spectrum of a class of algebras is the function that counts, up to isomorphism, the number of at most k -generated algebras in the class, for k =1,2,… . We consider the G -spectra of the varieties of algebras generated by a single two-element algebra. We show that such spectra are either polynomial, exponential, or at least doubly exponential as a function of k . For the varieties that have polynomial or exponential G -spectra we provide an exact formula for the function.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196700000121

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