

A370389


Number of distinct multisets of cycle lengths in the cell mapping schemes in extended selforthogonal diagonal Latin squares of order n.


0



1, 4, 4, 4, 5, 15, 16, 19, 20, 43, 48, 57, 63
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OFFSET

1,2


COMMENTS

A cells mapping scheme (CMS) for an ordered pair (A,B) of Latin squares is a permutation p of N^2 integer numbers from 0 to N^21 such that p[i] = j, 0 <= i, j <= N^21 iff A[i] = B[j] (square’s elements are listed lefttoright and toptobottom in the string representation). Used for getting ESODLS (see A309210). Structure of the multiset of cycle lengths in the CMS provides cycle of ESODLS with length equal to the least common multiple of cycle lengths in the CMS.
An extended selforthogonal diagonal Latin square (ESODLS) is a diagonal Latin square that has an orthogonal diagonal Latin square from the same main class (see A309598).


LINKS



EXAMPLE

For order n=5 there are 5 different multisets of cycle lengths for ESODLS CMS:
1. {1, 1, ..., 1} (25 times) = {1:25};
2. {1:5, 2:10};
3. {1:1, 4:6};
4. {1:1, 2:12};
5. {1:9, 2:8},
so a(5)=5.


CROSSREFS



KEYWORD

nonn,more,hard


AUTHOR



STATUS

approved



