Abstract
A hypergraph (
V,
E) defined on a linearly ordered set (
V, ⪯) is said to be
shift stable if
x∈
A∈
E,
y∉
A,
x⪯
y implies (
A⧹\s{
x\s})∪\s{
y\s}∈
E. It is shown here that a hypergraph is shift stable if and only if there is a real
t and a positive setfunction
c, which is monotonic, in some sense, with respect to the linear order ⪯, such that a set
A⊆
V belongs to the hypergraph if and only if the sum of
c(
B)s for the subsets
B⊂
A of size |
A|−1 is at least
t.