Pensieve Header: An attempt on the ribbon property using Γ-calculus.

dir=SetDirectory["C:/drorbn/AcademicPensieve/2014-05/"];
<< KnotTheory`
<< MetaCalculi/MetaCalculi-Program.m

n=4; γ=Γ[ω1, (∑_(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])]

ϵ[1]ϵ[2] // Γ

cert = γ // dm[1,2,1] // dm[3,4,2]

eqns=(ϵ[1]ϵ[2] // Γ)==(cert /. (Subscript[σ, _])->1) // Simplify

alex=(γ // dm[4,3,3] // dm[3,2,2] // dm[2,1,1])[[1]]

Simplify[alex, eqns]

Simplify[cert[[1]]]