A286317 Number of species of partial Latin squares of size n.

1, 2, 5, 18, 59, 306, 1861, 15097, 146893, 1693416, 22239872, 327670703

Offset: 1

Author

Ian Wanless, May 06 2017

Keywords

• nonn
• more

Comments

The size of a partial Latin square (PLS) is the number of filled entries, not the order of the matrix. The species of a PLS are all those PLSs you can get by permuting the rows, columns and symbols, and also by permuting these three roles themselves. Empty rows and columns are ignored.

Links

• H. Dietrich and I. M. Wanless, Small partial Latin squares that embed in an infinite group but not into any finite group, J. Symbolic Comput., Volume 86, May-June 2018, Pages 142-152. DOI 10.1016/j.jsc.2017.04.002.
• Raúl M. Falcón, Rebecca J. Stones, Enumerating partial Latin rectangles, arXiv:1908.10610 [math.CO], 2019.

Crossrefs

Cf. A003090 (analog of this sequence, but for completed Latin squares), A286318 (for the same objects as this sequence, but with the extra requirement of being connected).