A286318 Number of species of connected partial Latin squares of size n.

1, 1, 3, 11, 36, 213, 1405, 12274, 125235, 1490851, 20003121, 299274006

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. A PLS is connected if its associated graph (entries are vertices and edges show which entries share their row column or symbol) is connected.

References

• 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., to appear. DOI 10.1016/j.jsc.2017.04.002.

Crossrefs

Cf. A286317 (is for the same objects but without the requirement to be connected).