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<p>The braid alternation number of a knot <i>K</i>, denoted by <i>Balt</i>(<i>K</i>), is an invariant that measures how far a link is from being an alternating closed braid; it resembles the alternation number invariant. However, although some relationships with other invariants have been given, the value of this invariant is still unknown for some alternating knots with a few crossings. In this article, we expand upon the previously given estimation of the braid alternation number by calculating it for the case of most ten-crossing knots. We also provide some criteria for improving the tabulation.</p>

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Braid alternation number of ten-crossing prime knots

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月23日

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  • María de los Angeles Guevara-Hernández,
  • Hugo Cabrera-Ibarra,
  • Manuel Antonio Resendiz-Pérez

摘要

The braid alternation number of a knot K, denoted by Balt(K), is an invariant that measures how far a link is from being an alternating closed braid; it resembles the alternation number invariant. However, although some relationships with other invariants have been given, the value of this invariant is still unknown for some alternating knots with a few crossings. In this article, we expand upon the previously given estimation of the braid alternation number by calculating it for the case of most ten-crossing knots. We also provide some criteria for improving the tabulation.