Salem Numbers, Pisot Numbers, Mahler Measure, and Graphs

نویسندگان

  • James McKee
  • Chris Smyth
چکیده

We use graphs to define sets of Salem and Pisot numbers, and prove that the union of these sets is closed, supporting a conjecture of Boyd that the set of all Salem and Pisot numbers is closed. We find all trees that define Salem numbers. We show that for all integers n the smallest known element of the n-th derived set of the set of Pisot numbers comes from a graph. We define the Mahler measure of a graph, and find all graphs of Mahler measure less than 2 1 5 . Finally, we list all small Salem numbers known to be definable using a graph.

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منابع مشابه

Numbers , Pisot Numbers , Mahler Measure and Graphs

We use graphs to define sets of Salem and Pisot numbers, and prove that the union of these sets is closed, supporting a conjecture of Boyd that the set of all Salem and Pisot numbers is closed. We find all trees that define Salem numbers. We show that for all integers n the smallest known element of the n-th derived set of the set of Pisot numbers comes from a graph. We define the Mahler measur...

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عنوان ژورنال:
  • Experimental Mathematics

دوره 14  شماره 

صفحات  -

تاریخ انتشار 2005