Visualize dendriform grove sum commutativity using Tamari associahedron

tamari-grove-commutativity.jl

using Dendriform, LightGraphs, GraphPlot, Colors
function highlight_sum(a::Grove,b::Grove)
    d = a.degr + b.degr
    g = DiGraph(Int(Cn(d)))
    for i = 1:Int(Cn(d))
        u = Dendriform.posetnext(PBTree(d,i))
        for t in u
            add_edge!(g,i,treeindex(t))
        end
    end
    sum1 = a + b
    sum2 = b + a
    col = ones(Int,Cn(d))
    for i ∈ 1:sum1.size
        col[treeindex(sum1.Y[i,:])] += 1
    end
    for i ∈ 1:sum2.size
        col[treeindex(sum2.Y[i,:])] += 2
    end
    nodecolor = [colorant"grey77", colorant"orange", colorant"lightseagreen", colorant"salmon"]
    gplot(g,nodelabel=[1:Int(Cn(d))...],nodefillc=nodecolor[col])
end
function highlight_sum(a::Dendriform.NotGrove,b::Dendriform.NotGrove)
    highlight_sum(convert(Grove,a),convert(Grove,b))
end