Rules of discretization for Painlev\'e equations
  The discrete Painlev\'e property is precisely defined, and basic discretization rules to preserve it are stated. The discrete Painlev\'e test is enriched with a new method which perturbs the continuum limit and generates infinitely many no-log conditions. A general, direct method is provided to search for discrete Lax pairs. 
R. Conte (CEA Saclay) and M. Musette (VUB Brussels)