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Journal article
On the existence of partitioned incomplete Latin squares with five parts
Australasian Journal of Combinatorics, Vol.74, pp.46-60
74
2019
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.
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- Title
- On the existence of partitioned incomplete Latin squares with five parts
- Publication Details
- Australasian Journal of Combinatorics, Vol.74, pp.46-60
- Resource Type
- Journal article
- Publisher
- Centre for Discrete Mathematics & Computing; Austraila
- Series
- 74
- Format
- pdf
- Copyright
- The author(s). Released under the CC BY-ND 4.0 International License
- Identifiers
- 99380090301106600
- Academic Unit
- Mathematics and Statistics; Hal Marcus College of Science and Engineering
- Language
- English