论文标题
双层覆盖的渐近估计
Asymptotic estimates for double-coverings
论文作者
论文摘要
有限集合$ \ {a_1，a_2，\ ldots，a_ {p} \} $的集合说，如果每个$ a \ in \ cup_ {k = 1}^{p} a_k $的每个$ a \ in \ cup_ {k = 1}^{p} a_k $都包含在该集合的两组中。对于固定的整数$ l $和$ p $，让$μ__{l，p} $是带有$ \＃（a_k）= l $，$ k = 1,2，\ ldots，p $的双覆盖的等价类别的数量。我们将数量$μ__{l，p} $的渐近行为描述为$ p \ to \ infty $。结果适用于为Bonami-Kiener超收集不平等的替代方法。
A collection of finite sets $\{A_1, A_2,\ldots, A_{p}\}$ is said to be a double-covering if each $a\in \cup_{k=1}^{p}A_k$ is included in exactly two sets of the collection. For fixed integers $l$ and $p$, let $μ_{l,p}$ be the number of equivalency classes of double-coverings with $\#(A_k)=l$, $k=1,2,\ldots,p$. We characterize the asymptotic behavior of the quantity $μ_{l,p}$ as $p\to \infty$. The results are applied to give an alternative approach to the Bonami-Kiener hypercontraction inequality.
