## An inequality from the “Interlacing-1” paper

This question is in reference to this paper, http://annals.math.princeton.edu/wp-content/uploads/annals-v182-n1-p07-p.pdf (or its arxiv version, http://arxiv.org/abs/1304.4132) For the argument to work one seems to need that for the symmetric ±1 signing adjacency matrix of the graph, As, it holds that, max−root(∑s∈{0,1}mdet(xI−As))≤max−root(Es∈{0,1}m[det(xI−As)]) But why should this inequality be true? and the argument works because the polynomial on the … Read more