Extended Abstracts Fall 2012 by Juan González-Meneses Martin Lustig & Enric Ventura

Author:Juan González-Meneses, Martin Lustig & Enric Ventura
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(2) R is a thin tree with associated weights , S is a thin tree with associated weights , and the associated weights of R and S verify the equations

(1)

(2)

where l − 1 is the cardinal of the set , and

The proof of this result can be found in [4]. The following proposition proves the ‘if’ part of the theorem. For the ‘only if’ part, it suffices to show that the number of solutions to Eqs. (1) and (2) coincides with the number of words with and .

Proposition 2.

Let w(a,b) be a word in normal form with respect to the generating system {a,b} of ,

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