Khallil Berrekkal

activity

20232026

collaborators

4 papers

math.CO2026

A formal framework for higher-order spin models via hypergraphs, polymatroids, and the Tutte polynomial

Khallil Berrekkal, Joanna A. Ellis-Monaghan, Merijn Moody +1

We develop a rigorous mathematical framework for statistical mechanics models on hypergraphs, and give conditions for lifting the classical connection between Potts model partition…

math.CO2026

A Hypergraph Tutte Polynomial

Khallil Berrekkal, Joanna A. Ellis-Monaghan, Merijn Moody

We introduce a Tutte polynomial for hypergraphs, $T_{HG}$ , together with $T_{k}$ , a related Tutte polynomial for $k$ -polymatroids. Both invariants admit deletion--contractio…

math.CO2024

Deterministic approximate counting of colorings with fewer than $2Δ$ colors via absence of zeros

Ferenc Bencs, Khallil Berrekkal, Guus Regts

Let $Δ, q \geq 3$ be integers. We prove that there exists $η \geq 0.002$ such that if $q \geq (2 - η) Δ$ , then there exists an open set $U \subset C$ that contains the i…

math.PR2023

Near optimal bounds for weak and strong spatial mixing for the anti-ferromagnetic Potts model on trees