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Abstract We show that the solutions of ultradiscrete Painlevé equations satisfy contiguity relations just as their continuous and discrete counterparts. Our starting point are the relations for q-discrete Painlevé equations which we then proceed to ultradiscretise. In this paper we obtain results for the one-parameter q-PIII, the symmetric q-PIV and the q-PIV. These results show that there exists a perfect parallel between the properties of continuous, discrete and ultradiscrete Painlevé equations.

Contiguity relations for discrete and ultradiscrete Painleve equations