A new partition identity coming from complex dynamics
George E. Andrews, Rodrigo Alonso Perez
Abstract
We present a new identity involving compositions (i.e. ordered partitions of natural numbers). The Formula has its origin in complex dynamical systems and appears when counting, in the polynomial family \fc:z zd + c \, periodic critical orbits with equivalent itineraries. We give two different proofs of the identity; one following the original approach in dynamics and another with purely combinatorial methods.
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