Division sudokus: Invariants, enumeration and multiple partitions

A division sudoku is a latin square whose all six conjugates are sudoku squares. We enumerate division sudokus up to a suitable equivalence, introduce powerful invariants of division sudokus, and also study latin squares that are division sudokus with respect to multiple partitions at the same time....

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Bibliographic Details
Published in:arXiv.org 2021-01
Main Authors: Drápal, Aleš, Vojtěchovský, Petr
Format: Article
Language:English
Subjects:
Arrays
Enumeration
Invariants
Partitions
Online Access:Get full text
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Summary:A division sudoku is a latin square whose all six conjugates are sudoku squares. We enumerate division sudokus up to a suitable equivalence, introduce powerful invariants of division sudokus, and also study latin squares that are division sudokus with respect to multiple partitions at the same time. We use nearfields and affine geometry to construct division sudokus of prime power rank that are rich in sudoku partitions.
ISSN:2331-8422
DOI:10.48550/arxiv.2101.03995