OFFSET
1,2
COMMENTS
Equivalence is up to translation and reflection. Only translations and reflections that are subsets of {1..n} are included.
EXAMPLE
For n = 4 there are 6 sets (up to equivalence) that with their reflections and translations cover {1..4}:
{{1}, {2}, {3}, {4}};
{{1, 2}, {2, 3}, {3, 4}};
{{1, 3}, {2, 4}};
{{1, 2, 4}, {1, 3, 4}};
{{1, 2, 3}, {2, 3, 4}};
{{1, 2, 3, 4}}.
.
For n = 5 there are 8 sets (up to equivalence) that with their reflections and translations cover {1..5}:
{{1}, {2}, {3}, {4}, {5}};
{{1, 2}, {2, 3}, {3, 4}, {4, 5}};
{{1, 3}, {2, 4}, {3, 5}};
{{1, 2, 4}, {1, 3, 4}, {2, 3, 5}, {2, 4, 5}};
{{1, 2, 3}, {2, 3, 4}, {3, 4, 5}};
{{1, 2, 3, 5}, {1, 3, 4, 5}};
{{1, 2, 3, 4}, {2, 3, 4, 5}};
{{1, 2, 3, 4, 5}}.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Andrew Howroyd, Nov 07 2019
STATUS
approved