Martin Grüttmüller
Completing Partial Latin Squares with Prescribed Diagonals
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

05B15 Orthogonal arrays, Latin squares, Room squares

Abstract: This paper deals with completion of partial latin squares
$L=(l_{ij})$ of order $n$ with $k$ cyclically generated diagonals
($l_{i+t,j+t}= l_{ij}+t$ if $l_{ij}$ is not empty; with calculations
modulo $n$).
There is special emphasis on cyclic completion. Here, we
present results for $k=2,\ldots,7$ and odd $n \leq 21$, and
we describe the computational method used (hill-climbing).
Noncyclic completion is investigated in the cases $k=2,3$ or $4$ and
$n \leq 21$.
Keywords: partial latin squares, completion, cyclically generated