The numbers lead a dance: Mathematics of the Sestina

Alan Champneys, Poul G Hjorth, Harry Man

Research output: Chapter in Book/Report/Conference proceedingChapter in a book

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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 N of verses, other than 6, can a sestina-like poem be formed. That is, which N will the prescribed permutation lead to a poem of N 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.
Original languageEnglish
Title of host publicationNon-linear partial differential equations, mathematical physics, and stochastic analysis
Subtitle of host publicationthe Helge Holden anniversary volume
PublisherEuropean Mathematical Society
Number of pages17
ISBN (Electronic)9783037196861
ISBN (Print)9783037191866
Publication statusPublished - 2018

Publication series

NameEMS series of Congress reports


  • Permutation Groups
  • Iterative Maps
  • Chaotic Dynamics
  • Sestina Poetry


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