论文标题
在常规超图中计数独立集
Counting independent sets in regular hypergraphs
论文作者
论文摘要
在$ d $ r $ r $ r $ r $ rust的超图中，在$ n $顶点，哪些具有最多的独立套件？虽然图形的类似问题（最初是由格兰维尔提出的）现在已经得到了充分的理解，但尚不清楚正确的一般猜想应该是什么。我们在这里的目标是提出这样的概括。借给我们的猜想，我们通过采用KAHN的熵方法来验证它在“准双层”超图（在这种情况下看起来很自然的二分图的概括）的类别中。
Amongst $d$-regular $r$-uniform hypergraphs on $n$ vertices, which ones have the largest number of independent sets? While the analogous problem for graphs (originally raised by Granville) is now well-understood, it is not even clear what the correct general conjecture ought to be; our goal here is propose such a generalisation. Lending credence to our conjecture, we verify it within the class of `quasi-bipartite' hypergraphs (a generalisation of bipartite graphs that seems natural in this context) by adopting the entropic approach of Kahn.
