Salem numbers and Pisot numbers from stars

Citation

McKee JF, Rowlinson P & Smyth CJ (1999) Salem numbers and Pisot numbers from stars. In: Gyory K, Iwaniec H & Urbanowicz J (eds.) Number Theory in Progress: Proceedings of the International Conference on Number Theory organized by the Stefan Banach International Mathematical Center in Honor of the 60th Birthday of Andrzej Schinzel, Zakopane, Poland, June 30-July 9, 1997, Volume 1: Diophantine Problems and Polynomials. International Conference on Number Theory, Zakopane, Poland, 30.06.1997-09.07.1997. Berlin: Walter De Gruyter, pp. 309-319. http://www.degruyter.com/view/product/5136

Abstract
We use trees to construct families of algebraic integers. These include certain families of Salem numbers and of Pisot numbers, constructed from stars. The family of Pisot numbers we construct forms a proper closed subset of the set of all Pisot numbers. We show that this subset contains Pisot numbers of arbitrary trace. In particular, we exhibit a Pisot number of trace -- 5 and degree 141, 731, 565, 070, 951.