Sharpness of the Morton-Franks-Williams inequality for positive knots and links

Ilya Alekseev

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arXiv · 2211.16434

Sharpness of the Morton-Franks-Williams inequality for positive knots and links

Ilya Alekseev

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Abstract

We provide a combinatorial characterisation of positive diagrams satisfying the equality in the Morton-Franks-Williams bound for the degrees of the HOMFLY-PT polynomial. This characterisation allows generating with relative ease examples of diagrams realizing the crossing number, the braid index, and the maximal self-linking number. Besides, we suggest a conjecture concerning the sharpness of the Morton-Franks-Williams inequality for strongly quasipositive links.

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Ilya Alekseev. 2022-11-29. Sharpness of the Morton-Franks-Williams inequality for positive knots and links. https://arxiv.org/abs/2211.16434

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