Reductions of lattice mKdV to $q$-$\mathrm{P}_{VI}$
  This Letter presents a reduction of the lattice modified Korteweg-de-Vries equation that gives rise to a $q$-analogue of the sixth Painlev\'e equation. This new approach allows us to give the first ultradiscrete Lax representation of an ultradiscrete analogue of the sixth Painlev\'e equation. 
Christopher M. Ormerod
nlin.SI