Hi Dr Joshi

I have been working on your paper Acheiving Higher Order convergence for the prices of European options in Binomial trees.

While proving corollary 3.3 about final layer how can we find all the nodes in the final layer by moving up or down from the central node.

Plz guide me in this regard.

Moreover how can we say that in the final layer the total number of nodes will be even in case of recombining trees defined for odd number of steps.

kindly guide.