The set PLS(a, b; n) is the set of all partial latin squares of order n with a completed rows, b completed columns and all other cells empty. We identify reductions of partial latin squares in PLS(2, 3; n) by using permutations described by filled rows and intersections of filled rows and columns. We find that all partial latin squares in PLS(2, 3;n), where n is sufficiently large, can be completed if such a reduction can be completed. We also show that all partial latin squares in PLS(2, 3; n) where the intersection of filled rows and columns form a latin rectangle have completions for n ≥ 8.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:liu-163092 |
| Date | January 2020 |
| Creators | Göransson, Herman |
| Publisher | Linköpings universitet, Matematiska institutionen |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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