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A287644 Maximum number of transversals in a diagonal Latin square of order n. 4
1, 0, 0, 8, 15, 32, 133, 384, 2241 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

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

Every diagonal Latin square is a Latin square, so A287645(n) <= a(n) <= A090741(n). - Eduard I. Vatutin, Sep 20 2020

a(11)>=37851, a(12)>=16600, a(13)>=1030367, a(14)>=428296, a(15)>=2429398, a(16)>=14720910, a(17)>=1606008513, a(19)>=87656896891, a(23)>=452794797220965, a(25)>=41609568918940625. - Eduard I. Vatutin, Mar 08 2020

REFERENCES

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.

LINKS

Table of n, a(n) for n=1..9.

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

E. I. Vatutin, About the minimal and maximal number of transversals in a diagonal Latin squares of order 9 (in Russian).

Eduard Vatutin, Alexey Belyshev, Natalia Nikitina, and Maxim Manzuk, Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10, High-Performance Computing Systems and Technologies in Sci. Res., Automation of Control and Production (HPCST 2020), Communications in Comp. and Inf. Sci. book series (CCIS, Vol. 1304) Springer, Cham (2020), 127-146.

E. I. Vatutin, S. E. Kochemazov, and 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, M. O. Manzuk, N. N. Nikitina, and V. S. Titov, Central symmetry properties for diagonal Latin squares, Problems of Information Technology (2019) No. 2, 3-8.

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

Eduard I. Vatutin, Natalia N. Nikitina, and Maxim O. Manzuk, First results of an experiment on studying the properties of DLS of order 9 in the volunteer distributed computing projects Gerasim@Home and RakeSearch (in Russian).

Eduard I. Vatutin, Proving list.

Index entries for sequences related to Latin squares and rectangles

CROSSREFS

Cf. A090741, A287645, A287647, A287648.

Sequence in context: A123526 A083686 A293360 * A089954 A134020 A343141

Adjacent sequences:  A287641 A287642 A287643 * A287645 A287646 A287647

KEYWORD

nonn,more

AUTHOR

Eduard I. Vatutin, May 29 2017

EXTENSIONS

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

a(9) added by Eduard I. Vatutin, Sep 20 2020

STATUS

approved

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Last modified July 27 21:21 EDT 2021. Contains 346316 sequences. (Running on oeis4.)