|
|
A286318
|
|
Number of species of connected partial Latin squares of size n.
|
|
1
|
|
|
1, 1, 3, 11, 36, 213, 1405, 12274, 125235, 1490851, 20003121, 299274006
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
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.
|
|
LINKS
|
|
|
CROSSREFS
|
Cf. A286317 (is for the same objects but without the requirement to be connected).
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|