

A160366


Number of transposeisomorphism classes of selforthogonal Latin squares of order n.


3




OFFSET

1,4


COMMENTS

A selforthogonal Latin square (SOLS) is a Latin square orthogonal to its transpose. Two SOLS L and L' are (row,column)paratopic if a permutation p applied to the rows and columns of L and a permutation q applied to the symbol set of L transforms L into L', in which case (p,q) is called an (row,column)paratopism from L to L'. If p=q, then L and L' are transposeisomorphic. An (row,column)autoparatopism is an (row,column)paratopism that maps L onto itself. The number of transposeisomorphism classes of SOLS of order n may be determined by the formula sum_{L in I(n)} sum_{a in A(L)}y(a)/A(L) where I(n) is a set of (row,column)paratopism class representatives of SOLS of order n, A(L) is the set of (row,column)autoparatopism of L for which p and q are both of the same type (x_1,x_2,...,x_n) and y(a)=\prod_{i=1}^n x_i!i^{x_i}. A set of (row,column)paratopism class representatives may be found at www.vuuren.co.za > Repositories.


REFERENCES

G. P. Graham and C.E. Roberts, 2006. Enumeration and isomorphic classification of selforthogonal Latin squares, Journal of Combinatorial Mathematics and Combinatorial Computing, 59, pp. 101118.


LINKS

Table of n, a(n) for n=1..10.
A. P. Burger, M. P. Kidd and J. H. van Vuuren, 2010. Enumerasie van selfortogonale Latynse vierkante van orde 10, LitNet Akademies (Natuurwetenskappe), 7(3), pp 122.
A. P. Burger, M. P. Kidd and J. H. van Vuuren, Enumeration of isomorphism classes of selforthogonal Latin squares, Ars Combinatoria, 97, pp. 143152.
M. P. Kidd, A repository of selforthogonal Latin squares


CROSSREFS

Cf. A160365, A160367, A160368.
Sequence in context: A309558 A346104 A087463 * A160923 A201457 A111118
Adjacent sequences: A160363 A160364 A160365 * A160367 A160368 A160369


KEYWORD

hard,more,nonn


AUTHOR

Martin P Kidd, May 11 2009


EXTENSIONS

Class names corrected, references updated, and a link updated by Martin P Kidd, Aug 14 2010


STATUS

approved



