Projects per year
Abstract
Paratopism is a well-known action of the wreath product Sn – S3 on Latin squares of order n. A paratopism that maps a Latin square to itself is an autoparatopism of that Latin square. Let Par(n) denote the set of paratopisms that are an autoparatopism of at least one Latin square of order n. We prove a number of general properties of autoparatopisms. Applying these results, we determine Par(n) for n ≤ 17. We also study the proportion of all paratopisms that are in Par(n) as n → ∞.
Original language | English |
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Pages (from-to) | 51-74 |
Number of pages | 24 |
Journal | Journal of Combinatorial Designs |
Volume | 25 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Feb 2017 |
Keywords
- automorphism
- autoparatopism
- autotopism
- Latin square
- quasigroup
Projects
- 1 Finished
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Towards the prime power conjecture
Australian Research Council (ARC), Monash University
27/02/12 → 31/12/16
Project: Research