Revised minimum-dilatation conjecture for 10-strand pseudo-Anosov braids

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Let δ‾9\underline{\delta}_9 be the stated candidate value for the minimum dilatation of pseudo-Anosov braids with 9 strands, and let xx denote the variable in its defining polynomial. 10-strand minimum-dilatation conjecture. The minimum dilatation among pseudo-Anosov braids with 10 strands equals

δ‾9=∣x9−2x5−2x4+1∣.\underline{\delta}_9=\left|x^9-2x^5-2x^4+1\right|.

This revises Venzke's conjecture in the case n=10n=10, after the original prediction was shown to fail there. The remaining values of δn\delta_n are presented as an outstanding computational problem in the source.

References

Primary source

Chi Cheuk Tsang and Xiangzhuo Zeng, “Minimum dilatations of pseudo-Anosov braids”, arXiv:2412.01648 (2025).

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