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Additive Partitions and Continued Fractions

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Abstract

A set S of positive integers is avoidable if there exists a partition of the positive integers into two disjoint sets such that no two distinct integers from the same set sum to an element of S. Much previous work has focused on proving the avoidability of very special sets of integers. We vastly broaden the class of avoidable sets by establishing a previously unnoticed connection with the elementary theory of continued fractions.

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Authors and Affiliations

  1. Tellabs Research Center, One Kendall Square, Cambridge, MA, 02139

    Timothy Y. Chow

  2. Department of Mathematics, Rutgers University, New Brunswick, NJ, 08903

    Christopher D. Long

Authors
  1. Timothy Y. Chow
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  2. Christopher D. Long
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Chow, T.Y., Long, C.D. Additive Partitions and Continued Fractions. The Ramanujan Journal 3, 55–72 (1999). https://doi.org/10.1023/A:1009813309003

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