Mohamed Omar

collaborators

5 papers

math.CO2026

Multiple Distance Ramsey Bounds For Graphs in Euclidean Spaces

Ayşegül Kula, Mohamed Omar, Jonah Stockwell +1

For a finite set $A \subset R_{> 0}$ and a finite graph $H$ , let $χ_{H} (R^{n}; A)$ be the minimum number of colors required to color $R^{n}$ while avoiding a mon…

math.CO2026

On a Quadratic Relation Between Stanley-Wilf Limits and FÃ¼redi-Hajnal Limits

Mohamed Omar

For a permutation matrix $P$ , let $s_{P}$ denote its Stanley-Wilf limit, the exponential growth rate of the number of $n \times n$ permutation matrices avoiding $P$ . Let $c_{P}$ denote…

math.CO2026

Ehrhart Theory over Abelian Group Rings

Robert Davis, JesÃºs A. De Loera, Alexey Garber +3

We introduce a unified framework for Ehrhart theory in which lattice point enumerators take coefficients in an Abelian group ring, encoding substantially richer algebraic data than…

math.CO2026

Real Reliability Roots of Simple Graphs are Dense

Mohamed Omar

We prove that the closure of the real roots of all-terminal reliability polynomials is exactly $[- 1, 0] \cup {1}$ , resolving a conjecture of Brown and McMullin and refining the co…

math.CO2026

New Perspectives On The Unimodality Of Domination Polynomials

Mohamed Omar

The domination polynomial of a graph $G$ is given by $D (G, x) = \sum_{k = 0}^{n} d_{k} (G) x^{k}$ where $d_{k} (G)$ records the number of $k$ -element dominating sets in $G$ . A conjecture of Alik…