Ultradiscrete hypergeometric solutions to Painlevé cellular automata
Chris Ormerod
Abstract
We propose new solutions to the Painleve cellular automata that
do not and cannot be derived using the ultradiscretization
method. We consider a lift of these equations to a
non-archimedean valuation field in which we may relax the
subtraction free framework of previous explorations of the area.
Using such a method, we derive a set of hypergeometric solutions
to the Painleve equations which has long been thought impossible
to derive.
Keywords:
Ultradiscrete, Painleve, Hypergeometric, Tropical.
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