A370389 Number of distinct multisets of cycle lengths in the cell mapping schemes in extended self-orthogonal diagonal Latin squares of order n.
1, 4, 4, 4, 5, 15, 16, 19, 20, 43, 48, 57, 63
Offset: 1
Examples
For order n=5 there are 5 different multisets of cycle lengths for ESODLS CMS:
1. {1, 1, ..., 1} (25 times) = {1:25};
2. {1:5, 2:10};
3. {1:1, 4:6};
4. {1:1, 2:12};
5. {1:9, 2:8},
so a(5)=5.
Links
- Vatutin E.I., About the ESODLS CMS multisets of cycle lengths for orders 11-13 (in Russian).
- Vatutin E.I., Zaikin O.S., Manzuk M.O., and Nikitina N.N., Searching for Orthogonal Latin Squares via Cells Mapping and BOINC-Based Cube-And-Conquer, Communications in Computer and Information Science, 2021, Vol. 1510, pp. 498-512, DOI: 10.1007/978-3-030-92864-3_38.
- Vatutin E.I., Belyshev A.D., Nikitina N.N., and Manzuk M.O., Use of X-based diagonal fillings and ESODLS CMS schemes for enumeration of main classes of diagonal Latin squares (in Russian), Telecommunications, 2023, No. 1, pp. 2-16, DOI: 10.31044/1684-2588-2023-0-1-2-16.
- Vatutin E. and Zaikin O., Classification of Cells Mapping Schemes Related to Orthogonal Diagonal Latin Squares of Small Order, Lecture Notes in Computer Science, Vol. 14389, Springer, Cham., 2023, pp. 21-34, DOI: 10.1007/978-3-031-49435-2_2.
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