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The crossing number and maximal bridge length of a knot diagram

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A. Stoimenow

Geometric Topology · Submitted 2 Mar 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We give examples showing that Kidwell's inequality for the maximal degree of the Brandt-Lickorish-Millett-Ho polynomial is in general not sharp.

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arXiv IDmath/9903017 (version 1)
Pith IDMXFIXPV2, Pith's permanent record of this paper and its review
CitationA. Stoimenow. "The crossing number and maximal bridge length of a knot diagram." arXiv:math/9903017 (1999). https://pith.science/paper/MXFIXPV2
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,607 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.16 · human participants 0.02 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.86 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We give examples showing that Kidwell's inequality for the maximal degree of the Brandt-Lickorish-Millett-Ho polynomial is in general not sharp.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We give examples showing that Kidwell's inequality for the maximal degree of the Brandt-Lickorish-Millett-Ho polynomial is in general not sharp. result 0.86 0.91 0.76 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.52 · evidence from proof or derivation 0.49.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We give examples showing that Kidwell's inequality for the maximal degree of the Brandt-Lickorish-Millett-Ho polynomial is in general not sharp.

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