P. Ayre

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20152018

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math.CO2018

Lower bounds on the chromatic number of random graphs

Peter Ayre, Amin Coja-Oghlan, Catherine Greenhill

We prove that a formula predicted on the basis of non-rigorous physics arguments [Zdeborova and Krzakala: Phys. Rev. E (2007)] provides a lower bound on the chromatic number of spa…

math.CO2017

The satisfiability threshold for random linear equations

Peter Ayre, Amin Coja-Oghlan, Pu Gao +1

Let $A$ be a random $m \times n$ matrix over the finite field $F_{q}$ with precisely $k$ non-zero entries per row and let $y \in F_{q}^{m}$ be a random vector chosen independently of $A$ .…