1 citations · 1 across the 5 of their papers we have counts for
7 papers
Hilbert functions of filtered graphical zonotopal algebras
Boris Shapiro, Ilya Smirnov, Arkady Vaintrob
The external zonotopal algebra of a graph is generated by nilpotent vertex elements and determines the graphical matroid after deleting loops. Replacing these generators by $…
Regularity of Symbolic Powers of Co-Chordal Edge Ideals
Chwas Ahmed, Mohammed Rafiq Namiq
Let be a finite simple co-chordal graph with at least one edge, and let be its edge ideal. Over an arbitrary field, we prove that the symbolic powers of satisfy $…
The graded Betti numbers of truncation of ideals in polynomial rings
Chwas Ahmed, Ralf Fröberg, Mohammed Rafiq Namiq
Let , a graded algebra satisfies if is generated in degree , and the graded minimal resolution is linear the first steps,…
Quasi-forest simplicial complexes and almost Cohen-Macaulay
Chwas Ahmed, Amir Mafi, Mohammed Rafiq Namiq
In this paper we study the quasi-forest simplicial complexes and we define the concept of simplicial -cycle (denoted by ) and simplicial -point (denoted by $\m…
Sequentially Cohen-Macaulay Co-Chordal Graphs: Structure and Projective Dimension
Chwas Ahmed, Amir Mafi, Mohammed Rafiq Namiq
We introduce a class of chordal graphs called (,,,)-trees. A graph belongs to this class if and only if its clique complex is sequentially Cohen-Macaulay, pro…
Tonal partition algebras: fundamental and geometrical aspects of representation theory
Chwas Ahmed, Paul Martin, Volodymyr Mazorchuk
For we define tonal partition algebra over . We construct modules for over …
On the number of principal ideals in d-tonal partition monoids
Chwas Ahmed, Paul Martin, Volodymyr Mazorchuk
For a positive integer , a non-negative integer and a non-negative integer , we study the number of principal ideals; and the number o…