

A307170


Minimum number of partial loops in a diagonal Latin square of order n.


1




OFFSET

1,4


COMMENTS

A loop in a Latin square is a sequence of cells v1=L[i1,j1] > v2=L[i1,j2] > v1=L[i2,j2] > ... > v2=L[im,j1] > v1=L[i1,j1] of length 2*m that consists of a pair of values {v1, v2}. A partial loop is a loop with length < 2*n.


LINKS

Table of n, a(n) for n=1..7.
E. I. Vatutin, Discussion about properties of diagonal Latin squares at forum.boinc.ru (in Russian)
Index entries for sequences related to Latin squares and rectangles


EXAMPLE

For example, the square
2 4 3 5 0 1
1 0 4 3 2 5
0 2 5 4 1 3
5 3 0 1 4 2
4 5 1 2 3 0
3 1 2 0 5 4
has a loop
2 4 . . . .
. . . . . .
. 2 . 4 . .
. . . . . .
4 . . 2 . .
. . . . . .
consisting of the sequence of cells L[1,1]=2 > L[1,2]=4 > L[3,2]=2 > L[3,4]=4 > L[5,4]=2 > L[5,1]=4 > L[1,1]=2 with length 6 < 12.
The total number of loops for this square is 21, all of which are partial.


CROSSREFS

Cf. A307166, A307167.
Sequence in context: A254526 A156390 A059680 * A225951 A278711 A307841
Adjacent sequences: A307167 A307168 A307169 * A307171 A307172 A307173


KEYWORD

nonn,more


AUTHOR

Eduard I. Vatutin, Mar 27 2019


STATUS

approved



