Pensieve header: Full stitching as a determinant.

<< KnotTheory`
<< "C:/drorbn/AcademicPensieve/Projects/MetaCalculi/MetaCalculi-Program.m"

K0=Last@SXForm[K=Knot[8,18]]

Alexander[K][T]

(M=Γ[K0][A]) // MatrixForm

Det[
Drop[M+Normal[SparseArray[{Band[{1,2}]->-1},{16,16}]], -1,-1] /. (Subscript[T, _])->T
] // Simplify

Z[K]

(dm[1,11,1][dm[1,10,1][dm[1,9,1][dm[1,8,1][dm[1,7,1][dm[1,6,1][dm[1,5,1][dm[1,4,1][dm[1,3,1][dm[1,2,1][K0//Γ]]]]]]]]]])

M1=(dm[1,11,1][dm[1,10,1][dm[1,9,1][dm[1,8,1][dm[1,7,1][dm[1,6,1][dm[1,5,1][dm[1,4,1][dm[1,3,1][dm[1,2,1][K0//Γ]]]]]]]]]])[A]

((1-(Subscript[T, 1])-(Subscript[T, 13])+(Subscript[T, 1]) (Subscript[T, 13])+(Subscript[T, 1]) (Subscript[T, 15]))/(Subscript[T, 15]))Det[
Drop[M1+Normal[SparseArray[{Band[{1,2}]->-1},{6,6}]], -1,-1]
]  /. (Subscript[T, _])->T // Simplify

n=6; γ0=Γ[1, (∑_(a=0)^n)(Subscript[h, a])(Subscript[σ, a]), (∑_(a=1)^n)(∑_(b=1)^n)(Subscript[t, a])(Subscript[h, b])(Subscript[α, 10a+b])]

t1=Det[
Drop[Normal[SparseArray[{Band[{1,2}]->1},{n,n}]]-γ0[A], -1,1]
]

t2=γ0;
Do[t2=t2 // dm[1,k,1], {k,2,n}];
t2=t2@ω

t1-t2 // Expand