Acyclic sets of linear orders: A progress report

  title={Acyclic sets of linear orders: A progress report},
  author={Peter C. Fishburn},
  journal={Social Choice and Welfare},
Let f ðnÞ be the maximum cardinality of an acyclic set of linear orders on f1; 2; . . . ; ng. It is known that f ð3Þ 1⁄4 4, f ð4Þ 1⁄4 9, f ð5Þ 1⁄4 20, and that all maximum-cardinality acyclic sets for na 5 are constructed by an ‘‘alternating scheme’’. We outline a proof that this scheme is optimal for n 1⁄4 6, where f ð6Þ 1⁄4 45. It is known for large n that f ðnÞ > ð2:17Þ and that no maximum-cardinality acyclic set conforms to the alternating scheme. Ran Raz recently proved that f ðnÞ < c for… CONTINUE READING