The four-way intersection problem for latin squares

Abstract

For $\mu$ given latin squares of order $n$, they have {\sf $k$ intersection} when they have $k$ identical cells and $n^2-k$ cells with mutually different entries. For each $n\ge 1$ the set of integers $k$ such that there exist $\mu$ latin squares of order $n$ with $k$ intersection is denoted by $I^{\mu }[n]$. In a paper by P. Adams et al. (2002), $I^3[n]$ is determined completely. In this paper we completely determine $I^4[n]$ for $n\ge 16$. For $n\le 16$, we find out most of the elements of $I^4[n]$.

Fixing a wrong expression in the definition $J^4[n]$, at beginning of Section 3 (Main results), page 11