Geodesic
The semimeander crossing number of knots and related invariants
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 13, Tome 476 (2018), pp. 20-33 Cet article a éte moissonné depuis la source Math-Net.Ru

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The minimum number of crossings among all of the diagrams of a knot $K$ composed of at most $k$ smooth simple arcs is called the $k$-arc crossing number of $K$. This number is denoted by $\mathrm{cr}_k(K)$. The $2$-arc crossing number is also called the semimeander crossing number. The article studies connections of the $k$-arc crossing numbers with the classical crossing number $\mathrm{cr}(K)$ of $K$. It is proved that for each knot $K$, the following inequalities are fulfilled: $\mathrm{cr}_2(K) \leqslant \sqrt[4]{6}^{\mathrm{cr}(K)}$ and $\mathrm{cr}_k(K) \leqslant \mathrm{cr}_{k+1}(K) + \frac{(\mathrm{cr}_{k+1}(K))^2} {2(k+1)^2}$. 
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     title = {The semimeander crossing number of knots and related invariants},
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Yu. S. Belousov. The semimeander crossing number of knots and related invariants. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 13, Tome 476 (2018), pp. 20-33. http://geodesic.mathdoc.fr/item/ZNSL_2018_476_a1/

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