Journal of Integer Sequences, Vol. 23 (2020), Article 20.1.2

Enumerating Diagonal Latin Squares of Order Up to 9

Stepan Kochemazov and Oleg Zaikin
Lermontov street 134
664033 Irkutsk

Eduard Vatutin
Southwest State University
50 let Oktyabrya 94
305040 Kursk Russia

Alexey Belyshev
Nakhimov Avenue 36 Building 1
117218 Moscow


We propose an algorithm for enumerating diagonal Latin squares. It relies on specific properties of diagonal Latin squares to employ symmetry breaking techniques. Furthermore, the algorithm employs several heuristic optimizations and bit arithmetic techniques. We use the algorithm to enumerate diagonal Latin squares of order at most 9.

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(Concerned with sequences A002182 A004394 A040047 A323256 A323257.)

Received July 3 2019; revised versions received October 8 2019; October 28 2019. Published in Journal of Integer Sequences, December 28 2019.

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