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bibkey: cheigh2022towards authors: Justin Cheigh and Guilherme Zeus Dantas e Moura and Ryan Jeong and Jacob Lehmann Duke and Wyatt Milgrim and Steven J. Miller and Prakod Ngamlamai year: 2022 title: Towards the Gaussianity of Random Zeckendorf Games doi: 10.48550/arXiv.2210.11038 claim: A uniform summable strong-mixing bound on the split indicators of the random Zeckendorf game would yield a Gaussian limit for the game length. strata_touched:

  • D5/S1/Digit/Carry
  • D5/S0/Rewriting/NewmanConfluence
  • D5/S0/Asymptotics/WeightedProbability/BinomialMomentIdentity
  • D5/S0/Asymptotics/WeightedProbability/SecondMomentCoherence license: citation-only triage: anchor

Towards the Gaussianity of Random Zeckendorf Games

Cheigh and coauthors study the number of moves in the random Zeckendorf game. Their Conjecture 1.7 asserts a Gaussian limit with expectation and variance approximately 0.215N. The paper proves Gaussianity only on certain partition components and states that extending it to the whole space is unclear; its open section converts that obstacle into Question 6.5, asking for a uniform summable strong-mixing bound, and the stronger pointwise Question 6.6. An affirmative answer to Question 6.5 yields the conjecture through a mixing central limit theorem.

This note is the literature anchor for the problem candidate Problems/random-zeckendorf-game-gaussianity.md.

Search log

  • 2026-08-18: Queried the arXiv Atom API for id_list=2210.11038. HTTP 200 with totalResults=1; the entry resolved to http://arxiv.org/abs/2210.11038v1, title Towards the Gaussianity of Random Zeckendorf Games, seven authors as recorded above, published 2022-10-20, primary category math.CO. The API reported no arxiv:doi and no arxiv:journal_ref, so the arXiv-assigned DOI is used.
  • 2026-08-18: Issued HEAD https://doi.org/10.48550/arXiv.2210.11038, which returned HTTP 302 redirecting to https://arxiv.org/abs/2210.11038.

No literature search for a later resolution of Conjecture 1.7 or Questions 6.5/6.6 was performed; the open status recorded in the problem candidate is the status stated in this arXiv version.

Verified locator

  • arXiv: https://arxiv.org/abs/2210.11038
  • DOI: https://doi.org/10.48550/arXiv.2210.11038