9 papers
On Alternateness of the Jones-Kauffman Polynomial of Virtual Links
Hamid Abchir, Khaled Qazaqzeh, Mohammed Sabak
We study alternateness of the Jones-Kauffman polynomial of virtual links. In particular, we identify a class of virtual links with alternating Jones-Kauffman polynomial that will b…
A New Polynomial for Checkerboard-Colorable 4-Valent Virtual Graphs
Hamid Abchir, Khaled Qazaqzeh, Mohammed Sabak
We assign a new polynomial to any checkerboard-colorable 4-valent virtual graph in terms of its Euler circuit expansion. This provides a new combinatorial formulation of the Kauffm…
On left-orderability of involutory quandles of links
Hamid Abchir, Mohammed Sabak
We give a non-left-orderability criterion for involutory quandles of non-split links. We use this criterion to show that the involutory quandle of any non-trivial alternating link…
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…
Infinite families of non-left-orderable L-spaces
Hamid Abchir, Mohammed Sabak
For each connected alternating tangle, we provide an infinite family of non-left-orderable L-spaces. This gives further support for Conjecture [3] of Boyer, Gordon, and Watson that…
On -para-Kähler Lie algebras a subclass of -symplectic Lie algebras
Hamid Abchir, Ilham Ait Brik, Mohamed Boucetta
-Para-Kähler Lie algebras are a generalization of para-Kähler Lie algebras and constitute a subclass of -symplectic Lie algebras. In this paper, we show that the char…
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…
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…
Analytic Linear Lie rack Structures on Leibniz Algebras
Hamid Abchir, Fatima-Ezzahrae Abid, Mohamed Boucetta
A linear Lie rack structure on a finite dimensional vector space is a Lie rack operation pointed at the origin and such that for any , the left transl…