Title: Partial progress on enumerating K5 descendants
|Affiliation:||University of Waterloo|
We call a particular operation on a graph which converts one triangle into two triangles a double triangle expansion, and call all those graphs which can be obtained from repeated double triangle expansions of a fixed graph the double triangle descendants of the graph. The class of double triangle descendants of the graph K5 seem to be a very important class of graphs for quantum field theory. Notably a conjecture of Brown and Schnetz says they are special since they appear to be precisely those graphs where a particular arithmetic invariant, the c2 invariant, is -1 for all primes. Consequently it is interesting to enumerate double triangle descendants of K5. I will describe some partial results in this directions.
This is joint work with Marni Mishna and Mohamed Laradji.
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