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Among all bi-Perron numbers, we characterise those all of whose Galoisconjugates are real or unimodular as the ones that admit a power which is thestretch factor of a pseudo-Anosov homeomorphism arising from Thurston'sconstruction. This is in turn equivalent to admitting a power which is thespectral radius of a bipartite Coxeter transformation.

The geometry of bi-Perron numbers with real or unimodular Galois conjugates