13 citations · 64 across the 26 of their papers we have counts for
28 papers
New relations for the vertex polynomial
Scott Baldridge, Ben McCarty
We extend the vertex polynomial to graphs of arbitrary degree and prove local relations that hold when a graph contains a digon, triangle, quadrilateral or pentagon.
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…
Quantum state systems that count perfect matchings
Scott Baldridge, Ben McCarty
In this paper we show how to categorify the -color vertex polynomial, which is based upon one of Roger Penrose's formulas for counting the number of -edge colorings of a plan…
A state sum for the total face color polynomial
Scott Baldridge, Louis H. Kauffman, Ben McCarty
The total face color polynomial is based upon the Poincaré polynomials of a family of filtered -color homologies. It counts the number of -face colorings of ribbon graphs for…