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Among all bi-Perron numbers, we characterise those all of whose Galois conjugates are real or unimodular as the ones that admit a power that is the stretch factor of a pseudo-Anosov homeomorphism arising from Thurston’s construction. This is in turn equivalent to admitting a power that is the spectral radius of a bipartite Coxeter transformation.

The Geometry of Bi-Perron Numbers with Real or Unimodular Galois Conjugates