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## Henry Bushby Transcription Pages

### VM533B94v6_267.jpg

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267

are represented by S_{n} ^{b}⁄_{c}, so in K

they are represented by K_{n} ^{a}⁄_{c},

where __a__ stands for arcs. (In

neither case do these expressions in-

dicate fractions.)

Thus the Torsion Knot corresponding

to S_{4} ^{6b}⁄_{18c} is K_{4} ^{6a}⁄_{18c}

[A right-facing arrow in the left margin]

(ix.[gamma]) The analogy is so complete that

the algebraical deductions made for

S in ii.p263ff, apply __mutatis mutandis__

to K.

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(x.) Whereas in S all the knots are

irreducible to knots with fewer crossings

in every series in K (except K_{1})

the~~re is one~~ Torsion Knots ~~(perhaps~~^ *in which a*

*is less than*reducible to

__n__arein

*a*preceding series. The formula

indicating the pairs of knots is :-

p266.i.

[The following two expressions are deleted by a wavy line]

K

_{n}

^{(n-1) a}⁄

_{(n-1)2 c}= K

_{(n-1)}

^{na}⁄

_{[(n-1)2 -1]c}