2 citations · 4 across the 10 of their papers we have counts for
5 papers · 1 filter
Singquandles, Psyquandles and Singular Knots: A Survey
Jose Ceniceros, Indu R. Churchill, Mohamed Elhamdadi +1
In this short survey we review recent results dealing with algebraic structures (quandles, psyquandles, and singquandles) related to singular knot theory. We first explore the sing…
Cocycle Invariants and Oriented Singular Knots
Jose Ceniceros, Indu R. Churchill, Mohamed Elhamdadi +1
We extend the quandle cocycle invariant to oriented singular knots and links using algebraic structures called \emph{oriented singquandles} and assigning weight functions at both r…
Big Data Approaches to Knot Theory: Understanding the Structure of the Jones Polynomial
Jesse S F Levitt, Mustafa Hajij, Radmila Sazdanovic
We examine the structure and dimensionality of the Jones polynomial using manifold learning techniques. Our data set consists of more than 10 million knots up to 17 crossings and t…
Framed Knots
Mohamed Elhamdadi, Mustafa Hajij, Kyle Istvan
This article gives a foundational account of various characterizations of framed links in the -sphere.
-Series and Quantum Spin Networks
Mohamed Elhamdadi, Mustafa Hajij, Jesse S F Levitt
The tail of a quantum spin network in the two-sphere is a -series associated to the network. We study the existence of the head and tail functions of quantum spin networks color…