26 citations · 58 across the 17 of their papers we have counts for
7 papers · 1 filter
Equivalence of edge bicolored graphs on surfaces
Oliver T. Dasbach, Heather M. Russell
Consider the collection of edge bicolorings of a graph that is cellularly embedded on an orientable surface. In this work, we count the number of equivalence classes of such colori…
Dehn coloring and the dimer model for knots
Alexander Madaus, Maisie Newman, Heather M. Russell
Fox coloring provides a combinatorial framework for studying dihedral representations of the knot group. The less well-known concept of Dehn coloring captures the same data. Recent…
Chebyshev polynomials and the Frohman-Gelca formula
Hoel Queffelec, Heather M. Russell
Using Chebyshev polynomials, C. Frohman and R. Gelca introduce a basis of the Kauffman bracket skein module of the torus. This basis is especially useful because the Jones-Kauffman…
A reduced set of moves on one-vertex ribbon graphs coming from links
Susan Abernathy, Cody Armond, Moshe Cohen +5
Every link in R^3 can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams.
A twisted dimer model for knots
Moshe Cohen, Oliver T. Dasbach, Heather M. Russell
We develop a dimer model for the Alexander polynomial of a knot. This recovers Kauffman's state sum model for the Alexander polynomial using the language of dimers. By providing so…
A topological construction for all two-row Springer varieties
Heather M. Russell
Springer varieties appear in both geometric representation theory and knot theory. Motivated by knot theory and categorification Khovanov provides a topological construction of $(n…