4 papers · 1 filter
The clock theorem for knotoids and linkoids
Neslihan Gügümcü, Louis H. Kauffman
In this paper, we generalize the \textit{Clock Theorem} of Formal Knot Theory to knotoids in . The clock theorem implies that clock states of a knotoid diagram form a lattice…
The Mock Alexander Polynomial for Knotoids and Linkoids
Joanna A. Ellis-Monaghan, Neslihan Gügümcü, Louis H. Kauffman +1
The mock Alexander polynomial is an extension of the classical Alexander polynomial, defined and studied for (virtual) knots and knotoids by the second and third authors. In this p…
Mock Alexander Polynomials
Neslihan Gügümcü, Louis H. Kauffman
In this paper, we construct mock Alexander polynomials for starred links and linkoids in surfaces. These polynomials are defined as specific sums over states of link or linkoid dia…
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…