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z%B%zoT;mfr#()v=00ve&L>LB+KF~1+6#743_)`XgMK2iJi5X(RjJe#T&fZ+cnEZu16oCb864~b|M3gJfFqh#P;fv*RTRh=0v3)$LV^2c zMCqGA2L{grbXcMd5s(fFE?$1q{S87O2s>Z~Boy3mAZ7?=sRKfTlZ9vof&4&ECTd3z)=UL6%v7kLGfu{0qz?J!ecUBXJ_z%6d_gtzaFotIoUXa*PufGTq^=5LjU(} pue7u> - -- Label each crossing with a number in order -- For each component: - - Walk along it from the starting point in its orientation - - At each crossing, write a tuple with components - - +i or -i if this is an over-crossing or under-crossing - - +1 or -1 if this is a left-handed or right-handed -``` Converting one code to the other is not too much work as one just need to first do a labelling step to convert crossing labels and then convert the over/under-strand and left/right-handedness relations between the two notations. @@ -579,8 +585,6 @@ So PD codes are simpler and compact to store (and generate from a diagram) but S // ), // $ -#pagebreak() - == Link reconstruction from code We briefly mention that reconstructing a link from a PD or SG code is not trivial and there are various approaches used by various softwares that can be used for this task. @@ -616,6 +620,8 @@ Another approach used by #link("https://knotfol.io/")[KnotFolio] is based on #li This condition that every point is the average of its neighbors can be easily expressed as a system of linear equations where some points on a chosen outer face have been fixed. When the graph is planar and 3-vertex-connected the linear system is non degenerate and has a unique solution. +#pagebreak() + = Computing the Polynomial Let's now recap the main formal algorithm for computing the Kauffman polynomial. diff --git a/theme.typ b/theme.typ index 6a11304..2a62d81 100644 --- a/theme.typ +++ b/theme.typ @@ -13,6 +13,7 @@ #let ams-article( // The article's title. title: [Paper title], + page-title: [Paper title], // An array of authors. For each author you can specify a name, // department, organization, location, and email. Everything but // but the name is optional. @@ -64,7 +65,7 @@ if i == 1 { return } set text(size: script-size) align(center)[ - #upper(title) + #upper(page-title) ] },