English

A fast coset-translation algorithm for computing the cycle structure of Comer relation algebras over $\mathbb{Z}/p\mathbb{Z}$

Combinatorics 2018-01-09 v2 Data Structures and Algorithms

Abstract

Proper relation algebras can be constructed using Z/pZ\mathbb{Z}/p\mathbb{Z} as a base set using a method due to Comer. The cycle structure of such an algebra must, in general, be determined \emph{a posteriori}, normally with the aid of a computer. In this paper, we give an improved algorithm for checking the cycle structure that reduces the time complexity from O(p2)\mathcal{O}(p^2) to O(p)\mathcal{O}(p).

Keywords

Cite

@article{arxiv.1708.04974,
  title  = {A fast coset-translation algorithm for computing the cycle structure of Comer relation algebras over $\mathbb{Z}/p\mathbb{Z}$},
  author = {Jeremy F. Alm and Andrew Ylvisaker},
  journal= {arXiv preprint arXiv:1708.04974},
  year   = {2018}
}
R2 v1 2026-06-22T21:16:22.292Z