cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A279648 Rows of the self-orthogonal Latin squares of order 7, lexicographically sorted.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 3, 4, 2, 5, 6, 7, 1, 4, 7, 6, 3, 1, 2, 5, 6, 1, 5, 7, 2, 4, 3, 2, 5, 7, 6, 3, 1, 4, 7, 3, 1, 2, 4, 5, 6, 5, 6, 4, 1, 7, 3, 2, 1, 2, 3, 4, 5, 6, 7, 3, 4, 2, 5, 6, 7, 1, 5, 1, 6, 7, 3, 4, 2, 6, 7, 1, 3, 2, 5, 4, 2, 5, 4, 6, 7, 1, 3, 7, 3, 5, 1, 4, 2, 6, 4, 6, 7, 2, 1, 3, 5
Offset: 1

Views

Author

Colin Barker, Dec 16 2016

Keywords

Comments

An m X m Latin square consists of m sets of the numbers 1 to m arranged in such a way that no row or column contains the same number twice.
Two m X m Latin squares are orthogonal if no pair of corresponding elements occurs more than once.
A self-orthogonal Latin square is a Latin square that is orthogonal to its transpose.
There are 19353600 self-orthogonal Latin squares of order 7.

Examples

			The first four squares are:
1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7
3 4 2 5 6 7 1   3 4 2 5 6 7 1   3 4 2 5 6 7 1   3 4 2 5 6 7 1
4 7 6 3 1 2 5   5 1 6 7 3 4 2   5 7 6 1 3 2 4   5 7 6 1 3 2 4
6 1 5 7 2 4 3   6 7 1 3 2 5 4   6 1 7 2 4 3 5   6 1 7 3 2 4 5
2 5 7 6 3 1 4   2 5 4 6 7 1 3   2 5 1 3 7 4 6   2 5 4 6 7 1 3
7 3 1 2 4 5 6   7 3 5 1 4 2 6   7 3 4 6 1 5 2   7 3 1 2 4 5 6
5 6 4 1 7 3 2   4 6 7 2 1 3 5   4 6 5 7 2 1 3   4 6 5 7 1 3 2

Links

Crossrefs

Cf. A160368, A279649, A279650, A279849, A279850.

A279649 Rows of the self-orthogonal Latin squares of order 8, lexicographically sorted.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 3, 4, 1, 2, 6, 5, 8, 7, 4, 5, 7, 3, 8, 2, 1, 6, 6, 7, 5, 8, 3, 1, 2, 4, 7, 1, 4, 6, 2, 8, 5, 3, 5, 8, 6, 7, 1, 3, 4, 2, 8, 3, 2, 5, 4, 7, 6, 1, 2, 6, 8, 1, 7, 4, 3, 5, 1, 2, 3, 4, 5, 6, 7, 8, 3, 4, 1, 2, 6, 5, 8, 7, 4, 5, 8, 3, 7, 2, 6, 1, 6, 8, 5, 7, 3, 1, 4, 2, 8, 1, 4, 6, 2, 7, 3, 5, 5, 7, 6, 8, 1, 3, 2, 4, 2, 6, 7, 1, 8, 4, 5, 3, 7, 3, 2, 5, 4, 8, 1, 6
Offset: 1

Views

Author

Colin Barker, Dec 16 2016

Keywords

Comments

An m X m Latin square consists of m sets of the numbers 1 to m arranged in such a way that no row or column contains the same number twice.
Two m X m Latin squares are orthogonal if no pair of corresponding elements occurs more than once.
A self-orthogonal Latin square is a Latin square that is orthogonal to its transpose.
There are 4180377600 self-orthogonal Latin squares of order 8.

Examples

			The first four squares are:
1 2 3 4 5 6 7 8   1 2 3 4 5 6 7 8   1 2 3 4 5 6 7 8   1 2 3 4 5 6 7 8
3 4 1 2 6 5 8 7   3 4 1 2 6 5 8 7   3 4 1 2 6 5 8 7   3 4 1 2 6 5 8 7
4 5 7 3 8 2 1 6   4 5 8 3 7 2 6 1   4 6 7 3 2 8 1 5   4 6 8 3 2 7 5 1
6 7 5 8 3 1 2 4   6 8 5 7 3 1 4 2   5 7 6 8 1 3 2 4   5 8 6 7 1 3 4 2
7 1 4 6 2 8 5 3   8 1 4 6 2 7 3 5   6 8 5 7 3 1 4 2   6 7 5 8 3 1 2 4
5 8 6 7 1 3 4 2   5 7 6 8 1 3 2 4   7 1 4 5 8 2 6 3   8 1 4 5 7 2 3 6
8 3 2 5 4 7 6 1   2 6 7 1 8 4 5 3   8 3 2 6 7 4 5 1   2 5 7 1 4 8 6 3
2 6 8 1 7 4 3 5   7 3 2 5 4 8 1 6   2 5 8 1 4 7 3 6   7 3 2 6 8 4 1 5

Links

Crossrefs

Cf. A160368, A279648, A279650, A279849, A279850.

A279850 Rows of the 1440 self-orthogonal Latin squares of order 5, lexicographically sorted.

Original entry on oeis.org

1, 2, 3, 4, 5, 3, 4, 2, 5, 1, 4, 1, 5, 3, 2, 5, 3, 1, 2, 4, 2, 5, 4, 1, 3, 1, 2, 3, 4, 5, 3, 4, 5, 1, 2, 5, 1, 2, 3, 4, 2, 3, 4, 5, 1, 4, 5, 1, 2, 3, 1, 2, 3, 4, 5, 3, 5, 2, 1, 4, 5, 1, 4, 2, 3, 2, 4, 5, 3, 1, 4, 3, 1, 5, 2, 1, 2, 3, 4, 5, 3, 5, 4, 2, 1, 4, 1, 2, 5, 3, 5, 4, 1, 3, 2, 2, 3, 5, 1, 4
Offset: 1

Views

Author

Colin Barker, Dec 20 2016

Keywords

Comments

An m X m Latin square consists of m sets of the numbers 1 to m arranged in such a way that no row or column contains the same number twice.
Two m X m Latin squares are orthogonal if no pair of corresponding elements occurs more than once.
A self-orthogonal Latin square is a Latin square that is orthogonal to its transpose.

Examples

			The first few squares are:
1 2 3 4 5   1 2 3 4 5   1 2 3 4 5   1 2 3 4 5   1 2 3 4 5   1 2 3 4 5
3 4 2 5 1   3 4 5 1 2   3 5 2 1 4   3 5 4 2 1   4 3 1 5 2   4 3 5 2 1
4 1 5 3 2   5 1 2 3 4   5 1 4 2 3   4 1 2 5 3   2 4 5 3 1   5 4 2 1 3
5 3 1 2 4   2 3 4 5 1   2 4 5 3 1   5 4 1 3 2   5 1 4 2 3   3 1 4 5 2
2 5 4 1 3   4 5 1 2 3   4 3 1 5 2   2 3 5 1 4   3 5 2 1 4   2 5 1 3 4

Links

Crossrefs

Cf. A160368, A279648, A279649, A279650, A279849.

A279650 An idempotent self-orthogonal Latin square of order 11, read by rows.

Original entry on oeis.org

1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 3, 2, 1, 11, 10, 9, 8, 7, 6, 5, 4, 5, 4, 3, 2, 1, 11, 10, 9, 8, 7, 6, 7, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 4, 3, 2, 1, 11, 10, 9, 8, 7, 6, 5, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 7, 8, 7, 6, 5, 4, 3, 2, 1, 11, 10, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11
Offset: 1

Views

Author

Colin Barker, Dec 16 2016

Keywords

Comments

An m X m Latin square consists of m sets of the numbers 1 to m arranged in such a way that no row or column contains the same number twice.
Two m X m Latin squares are orthogonal if no pair of corresponding elements occurs more than once.
A self-orthogonal Latin square is a Latin square that is orthogonal to its transpose.
An m X m self-orthogonal Latin square is idempotent if the diagonal contains 1 to m in order.

Examples

			The Latin square is:
   1 11 10  9  8  7  6  5  4  3  2
   3  2  1 11 10  9  8  7  6  5  4
   5  4  3  2  1 11 10  9  8  7  6
   7  6  5  4  3  2  1 11 10  9  8
   9  8  7  6  5  4  3  2  1 11 10
  11 10  9  8  7  6  5  4  3  2  1
   2  1 11 10  9  8  7  6  5  4  3
   4  3  2  1 11 10  9  8  7  6  5
   6  5  4  3  2  1 11 10  9  8  7
   8  7  6  5  4  3  2  1 11 10  9
  10  9  8  7  6  5  4  3  2  1 11

Links

Crossrefs

Cf. A160368, A279648, A279649, A279849, A279850.
Showing 1-4 of 4 results.

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