38 citations · 199 across the 44 of their papers we have counts for
5 papers · 1 filter
On Rational Knots and Links in the Solid Torus
Khaled Bataineh, Mohamed Elhamdadi, Mustafa Hajij
We introduce the notion of rational links in the solid torus. We show that rational links in the solid torus are fully characterized by rational tangles, and hence by the continued…
Segmenting a Surface Mesh into Pants Using Morse Theory
Mustafa Hajij, Tamal Dey, Xin Li
A pair of pants is a genus zero orientable surface with three boundary components. A pants decomposition of a surface is a finite collection of unordered pairwise disjoint simple c…
Singular Knots and Involutive Quandles
Indu R. U. Churchill, M. Elhamdadi, M. Hajij +1
The aim of this paper is to define certain algebraic structures coming from generalized Reidemeister moves of singular knot theory. We give examples, show that the set of colorings…
Twist Regions and Coefficients Stability of the Colored Jones Polynomial
Mohamed Elhamdadi, Mustafa Hajij, Masahico Saito
We prove that the coefficients of the colored Jones polynomial of alternating links stabilize under increasing the number of twists in the twist regions of the link diagram. This g…
The Colored Jones Polynomial of Singular Knots
Khaled Bataineh, Mohamed Elhamdadi, Mustafa Hajij
We generalize the colored Jones polynomial to -valent graphs. This generalization is given as a sequence of invariants in which the first term is a one variable specialization o…