A394970 Number of isotopism classes of row-Hamiltonian Latin squares of order n.

1, 1, 1, 0, 1, 0, 2, 0, 64, 0, 1374132, 0

Offset

1,7

Comments

A Latin square is row-Hamiltonian if the permutation mapping row i to row j consists of a single cycle, for all distinct i,j. An isotopism class contains all the Latin squares obtainable by permuting rows, permuting columns and permuting symbols.

a(n) = 0 if n > 2 is even [Wanless].

References

J. Allsop and I.M. Wanless, Perfect 1-factorisations of K_{11,11}, Australasian J. Combinatorics 95 (2026), 114-130.

Links

Table of n, a(n) for n=1..12.

Example

The Cayley table of any cyclic group of prime order is a row-Hamiltonian Latin square.

Crossrefs

Cf. A394971, A120489.

Sequence in context: A140800 A012694 A264437 * A306061 A195209 A397280

Adjacent sequences: A394967 A394968 A394969 * A394971 A394972 A394973

Keyword

nonn,more

Author

Ian Wanless, Apr 08 2026

Status

approved