Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equilateral stick number of knots   An equilateral stick number $s_{=}(K)$ of a knot $K$ is defined to be the
minimal number of sticks required to construct a polygonal knot of $K$ which
consists of equal length sticks. Rawdon and Scharein [12] found upper bounds
for the equilateral stick numbers of all prime knots through 10 crossings by
using algorithms in the software KnotPlot. In this paper, we find an upper
bound on the equilateral stick number of a nontrivial knot K in terms of the
minimal crossing number $c(K)$ which is $s_{=}(K) \le 2c(K) + 2$. Moreover if
$K$ is a non-alternating prime knot, then $s_{=}(K) \le 2c(K) - 2$. Furthermore
we find another upper bound on the equilateral stick number for composite knots
which is $s_{=}(K_1 \# K_2) \le 2c(K_1) + 2c(K_2)$.

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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph