The existence of circular Florentine arrays

Research output: Contribution to journalArticle

Abstract

A k × n circular Florentine array is an array of n distinct symbols in k circular rows such that (1) each row contains every symbol exactly once, and (2) for any pair of distinct symbols (a, b) and for any integer m from 1 to n - 1 there is at most one row in which 6 occurs m steps to the right of a. For each positive integer n = 2,3,4,..., define Fc(n) to be the maximum number such that an Fc(n) × n circular Florentine array exists. From the main construction of this paper for a set of mutually orthogonal Latin squares (MOLS) having an additional property, and from the known results on the existence/nonexistence of such MOLS obtained by others, it is now possible to reduce the gap between the upper and lower bounds on Fc(n) for infinitely many additional values of n not previously covered. This is summarized in the table for all odd n up to 81.

Original languageEnglish
Pages (from-to)31-35
Number of pages5
JournalComputers and Mathematics with Applications
Volume39
Issue number11
DOIs
Publication statusPublished - 2000 Apr 20

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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