Paper Info
Title
On the existence of partitioned incomplete Latin squares with five parts
Abstract
Let a, b, c, d, and e be positive integers. In 1982 Heinrich showed the existence of a partitioned incomplete Latin square (PILS) of type (a, b, c) and (a, b, c, d) if and only if a = b = c and 2a >= d. For PILS of type (a, b, c, d, e) with a <= b <= c <= d <= e, it is necessary that a+ b+ c >= e, but not sufficient. In this paper we prove an additional necessary condition and classify the existence of PILS of type (a, b, c, d, a + b + c) and PILS with three equal parts. Lastly, we show the existence of a family of PILS in which the parts are nearly the same size.
Year
Venue
DocType
2019
AUSTRALASIAN JOURNAL OF COMBINATORICS
Journal
Volume
ISSN
Citations 
74
2202-3518
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Jaromy Kuhl1104.72
Donald McGinn200.68
Michael William Schroeder300.68