### 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 F_{c}(n) to be the maximum number such that an F_{c}(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 F_{c}(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 language | English |
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Pages (from-to) | 31-35 |

Number of pages | 5 |

Journal | Computers and Mathematics with Applications |

Volume | 39 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2000 Apr 20 |

### All Science Journal Classification (ASJC) codes

- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics