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
KEYWORD
nonn,more
AUTHOR
Pontus von Brömssen, Apr 07 2024
STATUS
approved