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On the variance of the Fibonacci partition function

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arxiv 2308.15415 v1 pith:6WIHCHKD submitted 2023-08-29 math.NT

classification math.NT
keywords fibonaccifunctionpartitionvarianceanswerdeterminedifferentdiophantine
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We determine the order of magnitude of the variance of the Fibonacci partition function. The answer is different to the most naive guess. The proof involves a diophantine system and an inhomogeneous linear recurrence.

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