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The image below is taken from a molecular biology textbook.

It is not clear to me that what is happening at the two writhe crossings matches up with the numbers provided.

Is there a problem with this example? And if not, is anyone able to explain (without using Calugareanu's Theorem, i.e. $\text{Lk}=\text{Tw}+\text{Wr}$) why the linking number is $23$? When I give the two strands orientations and half the sums of signs of crossings, I do not get $23$.

enter image description here

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  • $\begingroup$ Does this answer help? $\endgroup$ – canadianer Jan 5 '18 at 18:03
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    $\begingroup$ @canadianer I understand how to compute Lk, Tw and Wr, but I think the linking number in this particular example is not as clear as any of those in your answer, and I am seeking to verify whether or not this example is correct. I am having trouble around the two places where there is writhe. I am also using a different (but equivalent) definition of Lk - the one which gives orientations to the strands and signs to the crossings, as seen on the wikipedia page here: en.wikipedia.org/wiki/Linking_number $\endgroup$ – A. Goodier Jan 5 '18 at 23:37
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    $\begingroup$ Oh I see. Actually that picture is awful since it shows all four strands intertwined at the sites of duplex crossover (which is not what happens). $\endgroup$ – canadianer Jan 5 '18 at 23:54

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