The numbers lead a dance. Mathematics of the Sestina

  • Alan R. Champneys

    University of Bristol, UK
  • Poul G. Hjorth

    Technical University of Denmark, Kgs. Lyngby, Denmark
  • Harry Man

    Oxford Brookes University, UK
The numbers lead a dance. Mathematics of the Sestina cover
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Sestinas are poems of 39 lines comprising six verses of six lines each, and a three line final verse or ‘envoi’. The structure of the sestina is built around word repetition rather than strict rhyme. Each verse uses the same set line ending words, but in a permuted order. The form of the permutation is highly specific, and is equivalent to iteration of the tent map. This paper considers for which number NN of verses, other than 6, can a sestina-like poem be formed. That is, which NN will the prescribed permutation lead to a poem of NN verses where no two verses have the same order of their end words. In so doing, a link is found between permutation groups, chaotic dynamics, and Cunningham numbers.