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A293778
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Number of centrally symmetric diagonal Latin squares of order n.
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4
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OFFSET
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1,4
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COMMENTS
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Centrally symmetric diagon Latin square is a square with one-to-one correspondence between elements within all pairs a[i][j] and a[n-1-i][n-1-j] (numbering of rows and columns from 0 to n-1).
It seems that a(n)=0 for n=2 and n=3 (diagonal Latin squares of these sizes don't exist) and for n=2 (mod 4).
Every doubly symmetric diagonal Latin square also has central symmetry. The converse is not true in general. It follows that A292517(n) <= a(4n). - Eduard I. Vatutin, May 26 2021
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LINKS
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E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, M. O. Manzuk, N. N. Nikitina, V. S. Titov, Properties of central symmetry for diagonal Latin squares, High-performance computing systems and technologies, No. 1 (8), 2018, pp. 74-78. (in Russian)
E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, M. O. Manzuk, N. N. Nikitina, V. S. Titov, Central Symmetry Properties for Diagonal Latin Squares, Problems of Information Technology, No. 2, 2019, pp. 3-8. doi: 10.25045/jpit.v10.i2.01.
E. I. Vatutin, Special types of diagonal Latin squares, Cloud and distributed computing systems in electronic control conference, within the National supercomputing forum (NSCF - 2022). Pereslavl-Zalessky, 2023. pp. 9-18. (in Russian)
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FORMULA
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EXAMPLE
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0 1 2 3 4 5 6 7 8
6 3 0 2 7 8 1 4 5
3 2 1 8 6 7 0 5 4
7 8 6 5 1 3 4 0 2
8 6 4 7 2 0 5 3 1
2 7 5 6 8 4 3 1 0
5 4 7 0 3 1 8 2 6
4 5 8 1 0 2 7 6 3
1 0 3 4 5 6 2 8 7
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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STATUS
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approved
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