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A287644 Maximum number of transversals in a diagonal Latin square of order n. 3
1, 0, 0, 8, 15, 32, 133, 384 (list; graph; refs; listen; history; text; internal format)



Same as maximum number of transversals in a Latin square of order n except n = 3.

a(10) >= 5504 from Parker and Brown.


J. W. Brown et al., Completion of the spectrum of orthogonal diagonal Latin squares, Lecture notes in pure and applied mathematics, volume 139 (1992), pp. 43-49.

E. T. Parker, Computer investigations of orthogonal Latin squares of order 10, Proc. Sympos. Appl. Math., volume 15 (1963), pp. 73-81.


Table of n, a(n) for n=1..8.

Eduard I. Vatutin, Discussion about properties of diagonal Latin squares at forum.boinc.ru.

E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, Estimating of combinatorial characteristics for diagonal Latin squares, Recognition — 2017 (2017), pp. 98-100 (in Russian).

E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, S. Yu. Valyaev, Enumerating the Transversals for Diagonal Latin Squares of Small Order. CEUR Workshop Proceedings. Proceedings of the Third International Conference BOINC-based High Performance Computing: Fundamental Research and Development (BOINC:FAST 2017). Vol. 1973. Technical University of Aachen, Germany, 2017. pp. 6-14. urn:nbn:de:0074-1973-0.

E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, S. Yu. Valyaev, Using Volunteer Computing to Study Some Features of Diagonal Latin Squares. Open Engineering. Vol. 7. Iss. 1. 2017. pp. 453-460. DOI: 10.1515/eng-2017-0052

E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, S. Yu. Valyaev, V. S. Titov, Estimating the Number of Transversals for Diagonal Latin Squares of Small Order, Telecommunications. 2018. No. 1. pp. 12-21 (in Russian).

Index entries for sequences related to Latin squares and rectangles


Cf. A090741, A287645, A287647, A287648.

Sequence in context: A123526 A083686 A293360 * A089954 A134020 A197602

Adjacent sequences:  A287641 A287642 A287643 * A287645 A287646 A287647




Eduard I. Vatutin, May 29 2017


a(8) added by Eduard I. Vatutin, Oct 29 2017



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Last modified January 19 18:27 EST 2019. Contains 319309 sequences. (Running on oeis4.)