A new partition identity coming from complex dynamics

George E. Andrews; Rodrigo A. Pérez

doi:10.1007/s00026-005-0254-6

A new partition identity coming from complex dynamics

George E. Andrews, Rodrigo A. Pérez

Mathematics

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3 Scopus citations

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 { f_c : z → z^d + 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.

Original language	English (US)
Pages (from-to)	245-257
Number of pages	13
Journal	Annals of Combinatorics
Volume	9
Issue number	3
DOIs	https://doi.org/10.1007/s00026-005-0254-6
State	Published - Oct 2005

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1007/s00026-005-0254-6

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title = "A new partition identity coming from complex dynamics",

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.",

author = "Andrews, {George E.} and P{\'e}rez, {Rodrigo A.}",

note = "Funding Information: ∗Second author supported by an NSF Postdoctoral Fellowship in the Mathematical Sciences, grant DMS-0202519.",

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N2 - 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.

AB - 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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A new partition identity coming from complex dynamics

Abstract

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