 1950 Paul Federbush
 A Near Proof of Weak Graph Positivity, A new Property of Regular Random Groups
(25K, LaTeX)
Sep 10, 19

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. One deals with rregular 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 imatchings, and conjectured that as n
goes to infinity the fraction of graphs that satisfy Delta^k d(i)
for all k and i, approaches 1. Here Delta is the finite difference operator.
This conjecture we called the 'graph positivity conjecture'.
In this paper it is formally shown that for each i and k the
probability that Delta^k d(i) goes to 1 with n going to infinity.
We call this weaker result the 'weak graph positivity conjecture ( theorem )'.
A formalism of Wanless as systematized by Pernici is central to this effort.
Our result falls short of being a rigorous proof since we make a sweeping
conjecture ( computer tested ), of which we so far have only a portion of the proof.
 Files:
1950.src(
1950.comments ,
1950.keywords ,
85WGP.tex )