An Approximate Vertex-Isoperimetric Inequality for $r$-sets

[摘要] We prove a vertex-isoperimetric inequality for \([n]^{(r)}\), the set of all \(r\)-element subsets of \(\{1,2,\ldots,n\}\), where \(x,y \in [n]^{(r)}\) are adjacent if \(|x \Delta y|=2\). Namely, if \(\mathcal{A} \subset [n]^{(r)}\) with \(|\mathcal{A}|=\

[学科分类] 离散数学和组合数学

[关键词] discrete isoperimetric inequalities