Deformed cluster maps of type A2N

We extend recent work of the third author and Kouloukas by constructing deformations of integrable cluster maps corresponding to the Dynkin types A2N, lifting these to higher-dimensional maps possessing the Laurent property and demonstrating integrality of the deformations for N≤ 3. This provides the first infinite class of examples (in arbitrarily high rank) of such maps and gives information on the associated discrete integrable systems. Key to our approach is a ``local expansion'' operation on quivers which allows us to construct and study mutations in type A2N from those in type A2(N-1).