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Interesting Esoterica

Survey on fusible numbers
Article by Xu, Junyan
In collection: Easily explained
We point out that the recursive formula that appears in Erickson's presentation "Fusible Numbers" is incorrect, and pose an alternate conjecture about the structure of fusible numbers. Although we are unable to solve the conjecture, we succeed in establishing some basic properties...
URL: arxiv.org/abs/1202.5614
PDF: arxiv.org/pdf/1202.5614v1
Entry: read.somethingorotherwhatever.

arXiv.orgSurvey on fusible numbersWe point out that the recursive formula that appears in Erickson's presentation "Fusible Numbers" is incorrect, and pose an alternate conjecture about the structure of fusible numbers. Although we are unable to solve the conjecture, we succeed in establishing some basic properties of fusible numbers. We suggest some possible approaches to the conjecture, and list further problems in the final chapter.
Jeff Erickson

@esoterica One of my bugs that really should be better known. As far as I know, there's been zero progress on this problem since Xu's paper. (Open problem: What's the smallest fusible number larger than 3? Open problem that will probably never be answered: What's the smallest fusible number larger than 4?)

Nov 10, 2018, 12:04 AM·Public·Web
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