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We study elements of second order linear recurrence sequences $$(G_n)_{n= 0}^{\infty }$$(Gn)n=0∞ of polynomials in $${{\mathbb {C}}}[x]$$C[x] which are decomposable, i.e. representable as $$G_n=g\circ h$$Gn=g∘h for some $$g, h\in {{\mathbb… Click to show full abstract
We study elements of second order linear recurrence sequences $$(G_n)_{n= 0}^{\infty }$$(Gn)n=0∞ of polynomials in $${{\mathbb {C}}}[x]$$C[x] which are decomposable, i.e. representable as $$G_n=g\circ h$$Gn=g∘h for some $$g, h\in {{\mathbb {C}}}[x]$$g,h∈C[x] satisfying $$\deg g,\deg h>1$$degg,degh>1. Under certain assumptions, and provided that h is not of particular type, we show that $$\deg g$$degg may be bounded by a constant independent of n, depending only on the sequence.
Journal Title: manuscripta mathematica
Year Published: 2017
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