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A371828
Number of labeled n-vertex hypergraphs (or set systems) that have a solution to the One Up puzzle.
2
1, 2, 7, 54, 993, 48868
OFFSET
0,2
COMMENTS
Here, a hypergraph is a set of nonempty subsets (hyperedges) of the set of vertices.
The One Up puzzle on a polyomino is defined in A371476. On a hypergraph, the objective of the puzzle is to assign a positive integer to each vertex in such a way that the vertices of each hyperedge are assigned consecutive numbers starting at 1. In other words, the vertex of a hyperedge of size 1 must be assigned the number 1, the vertices of a hyperedge of size 2 must be assigned the numbers 1 and 2, etc.
EXAMPLE
The following hypergraphs have solutions to the One Up puzzle. Only one such hypergraph for each isomorphism class is given, with the size of the isomorphism class in parentheses.
n = 0 n = 1 n = 2 n = 3
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{} (1) {} (1) {} (1) {} (1)
{1} (1) {1} (2) {1} (3)
{12} (1) {12} (3)
{1,2} (1) {123} (1)
{1,12} (2) {1,2} (3)
{1,12} (6)
{1,23} (3)
{1,123} (3)
{12,13} (3)
{12,123} (3)
{1,2,3} (1)
{1,2,13} (6)
{1,12,13} (3)
{1,12,23} (6)
{1,12,123} (6)
{1,2,13,23} (3)
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a(n): 1 2 7 54
CROSSREFS
Cf. A371476, A371829 (unlabeled hypergraphs).
Sequence in context: A283335 A326207 A280221 * A227381 A182055 A358944
KEYWORD
nonn,more
AUTHOR
STATUS
approved