A collection of finite sets {A1β,A2β,β¦,Apβ} is said to be a
double-covering if each aββͺk=1pβAkβ is included in exactly two
sets of the collection. For fixed integers l and p, let ΞΌl,pβ be the
number of equivalency classes of double-coverings with #(Akβ)=l,
k=1,2,β¦,p. We characterize the asymptotic behavior of the quantity
ΞΌl,pβ as pββ. The results are applied to give an alternative
approach to the Bonami-Kiener hypercontraction inequality.Comment: 19 page