Markov's conjecture on integral necklaces

David Fisac

doi:10.1112/blms.70178

August 22, 2025Bulletin of the London Mathematical SocietyOpen Access

Markov's conjecture on integral necklaces

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Key Points

Markov's conjecture is expressed in combinatorial terms, revealing a unique set of lengths derived from its geometric perspective.
The main finding involves a geometric reformulation of the uniqueness conjecture related to modular torus lengths.
Analysis of the simple length spectrum provides explicit descriptions essential for understanding integral necklaces.
Discovering new interpretations may enhance insights into both combinatorial mathematics and geometric structures.

Abstract

We use the geometric reformulation of Markov's uniqueness conjecture in terms of the simple length spectrum of the modular torus to rewrite the conjecture in combinatorial terms by explicitly describing this set of lengths.

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David Fisac (2025) studied this question.

synapsesocial.com/papers/68af5707ad7bf08b1eadd996 https://doi.org/10.1112/blms.70178

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Markov's conjecture on integral necklaces

Key Points

Abstract

Discussion

Cite This Study

Markov's conjecture on integral necklaces

Key Points

Abstract

Discussion

Cite This Study

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