4 papers
New relations for the vertex polynomial
Scott Baldridge, Ben McCarty
The paper extends the vertex polynomial to graphs of any degree and establishes local relations that apply when a graph contains small cycles such as digons, triangles, quadrilater…
A counterexample for the polar conjecture of Spencer-Brown
Scott Baldridge, Louis H. Kauffman, Ben McCarty
In 1976, George Spencer-Brown announced a proof of the four color theorem, using operations on Tait colorings for trivalent plane graphs. In subsequent work he formulated these ope…
New relations for the Penrose polynomial
Scott Baldridge, Ben McCarty
We introduce two new relations involving the pentagon and the quadrilateral for the evaluation of the Penrose polynomial at that is proven using a new type of ribbon graph po…
A new way to prove configuration reducibility using gauge theory
Scott Baldridge, Ben McCarty
We show how ideas coming out of gauge theory can be used to prove configurations in the list of ``633 unavoidable configurations" are reducible. In this paper, we prove the smalles…