论文标题
图形阳性弱的证明，用于大量参数
A PROOF of Weak Graph Positivity, for a Large Range of the Parameters
论文作者
论文摘要
一个用2N顶点处理的是R-Trigular二分图。在以前的论文中，Butera，Pernici和作者引入了数量D（i），这是I匹配数量的函数，并猜想，对于所有k和i的delta n is Asher Is there delta is therta is of Delta is of Firta is n delta is in Infienta is in Infienta是无限的。这个猜想我们称为“图阳性猜想”。 "Weak graph positivity" is the conjecture that for each i and k the probability that Delta^k (d(i) is non-negative goes to 1 as n goes to infinity. Here we prove this for the range of parameters where r < 11, i+k < 101, k < 21, or i+k < 30 all r. A formalism of Wanless as systematized by Pernici is central to this effort.
One deals with r-regular bipartite graphs with 2n vertices. In a previous paper Butera, Pernici, and the author have introduced a quantity d(i), a function of the number of i-matchings, and conjectured that as n goes to infinity the fraction of graphs that satisfy Delta^k( d(i)) is non-negative, for all k and i, approaches 1. Here Delta is the finite difference operator. This conjecture we called the "graph positivity conjecture". "Weak graph positivity" is the conjecture that for each i and k the probability that Delta^k (d(i) is non-negative goes to 1 as n goes to infinity. Here we prove this for the range of parameters where r < 11, i+k < 101, k < 21, or i+k < 30 all r. A formalism of Wanless as systematized by Pernici is central to this effort.
