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math.GT2022
An Improvement of the lower bound for the minimum number of link colorings by quandles
Hamid Abchir, Soukaina Lamsifer
We improve the lower bound for the minimum number of colors for linear Alexander quandle colorings of a knot given in Theorem 1.2 of Colorings beyond Fox: The other linear Alexande…
math.GT2020
On the minimum number of Fox Colorings of Knots
Hamid Abchir, Mohamed Elhamdadi, Soukaina Lamsifer
We investigate Fox colorings of knots that are 17-colorable. Precisely, we prove that any 17-colorable knot has a diagram such that exactly 6 among the seventeen colors are assigne…
math.GT2020
Generating links that are both quasi-alternating and almost alternating
Hamid Abchir, Mohammed Sabak
We construct an infinite family of links which are both almost alternating and quasi-alternating from a given either almost alternating diagram representing a quasi-alternating lin…