Mathematical forms in poetry 4 – Permutations

Permutations are a feature of many poetic forms: rhyme and metrical patterns, the arrangement of lines in a villanelle or pantoum, the rotation of end-words through the stanzas of a sestina. Ruth Holzer’s ‘For Dylan Thomas on His Hundredth Birthday’ is an example of a sestina by a contemporary poet, with end-words wild, skyendhillswavelove.

The sestina form has given rise to many adaptations, such as Swinburne’s rhyming double sestina ‘The Complaint of Lisa’ or Marvin Thompson’s ‘Triptych’, in which each of the nine stanzas has seven lines. The American poet Marie Ponsot  invented a condensed form called the tritina, which consists of three tercets with three end-words in the sequence 123, 312, 213, and a single final line containing all three end-words. 

The French poet Raymond Queneau, cofounder of the Oulipo movement, was fascinated by the creative possibilities of using mathematics in his writing. In 1961 he published ‘Cent mille milliards de poémes’ (‘A Hundred Thousand Billion Poems’), a sequence of ten sonnets constructed in such a way that any given line from one sonnet can be interchanged at random with the corresponding line from any of the other sonnets. 

Francois Le Lionnais, co-founder with Queneau of the Oulipo movement, devised the concept of a multi-choice narrative, in which the reader can choose a route through a story or poem. JoAnne Growney shares a fine example of this approach on her blog ‘Intersections – Poetry with Mathematics’: ‘Multiple Choice’ by Harry Mathews is accompanied by a decision tree illustrating the possible paths.

Phil Vernon’s ‘Metro-man’, from his collection Poetry After Auschwitz, also offers a choice of routes through a poem.

The lipogram – a piece of writing in which certain letters of the alphabet are omitted – is another form of constrained writing that was taken up by the Oulipo movement, although its roots go back to ancient Greece. Experimental poet Luke Bradford’s Zoolalia is a collection of lipograms constrained by the letters that make up the Latin names of various animal species. 

An anagram is a special case of a lipogram, in which all the letters of a word or phrase are rearranged to form a different word or phrase. The Oulipian poet Michelle Grangaud specialises in anagrams: her book Stations is a collection of poems that are anagrams of the names of Paris metro stations.  She has invented a poetic form known as a sestanagrammatina, which is a combination of the sestina and the anagram. Each line in her sestina ‘Le grand incendie de Londres’is an anagram of the poem’s title.

Anthony Etherin has pushed the poetic possibilities of the anagram even further. The Utu Sonnets is a sequence of seven sonnets, each of which – in addition to other constraints – is an exact anagram of all the others. You can read my review of this remarkable work here.

In the 1950s the innovative artist, writer and sound poet Brion Gysin experimented with what is known as the cut-up technique, cutting up and rearranging pieces of text. This led him to write a series of permutation poems, each consisting of permutations of the words in the title. Together with the mathematician Ian Sommerville he pioneered the use of computer programming to generate permutated text: an early example of the application of technology in poetry.

Ancient traditions of bellringing, with their complex combinatorial patterns, have provided a stimulating resource for mathematical educator and poet Susan Gerofsky. In a 2018 paper co-authored with three others, she considers how the Plain Hunt on 4 can be used in a variety of creative applications, including the writing of poetry.  (In a fine example of multidisciplinary collaboration, Gerofsky and ceramic artist Nevena Tadic jointly created a beautiful ceramic mobile of Gerofsky’s ‘Desert Poem’.)

Stephanie Strickland’s innovative collection Ringing the Changes also draws on bell-ringing traditions. In place of bells, however, Strickland has used shareable code to generate text. Strickland gives us a sense of this approach in Liberty Ring! which she describes as ‘a toy interactive companion to Ringing the Changes’. With each ‘sounding’ of the bell (by clicking on it with the mouse cursor) a set of seven statements appears on the computer screen for us to read and contemplate, in an experience that is both playful and profound.

From ancient traditions and mediaeval troubadour songs to contemporary code-generated text, permutations and poetry interweave in creative works of dazzling virtuosity.  

Marian’s book From Fibs to Fractals: exploring mathematical forms in poetry, will be published by Beir Bua Press later this year.


Birken, Marcia and Coon, Anne C. (2008) Discovering Patterns in Mathematics and Poetry. Amsterdam, Rodopi.

Bonch-Osmolovskaya, Tatiana (2010) ‘Some Possibilities of Russian Combinatorial Literature’. Bridges 2010: Mathematics, Music, Art, Architecture, Culture. Available at

Bradford, Luke (2021) Zoolalia. Penteract Press

Champneys, A. R., Hjorth, P. G., & Man, H. (2018). ‘The numbers lead a dance: Mathematics of the Sestina’. In 

Non-linear partial differential equations, mathematical physics, and stochastic analysis: the Helge Holden anniversary volume (pp. 55-71). European Mathematical Society Publishing House. Available online at

Cramer, Florian (2000) ‘Combinatory Poetry and Literature in the Internet’. Available at 

Dumas, Jean-Guillaume. (2008). ‘Caractérisation des Quenines et leur représentation spirale. Mathématiques et sciences humaines’. 184. 10.4000/msh.10946. Available at:

Etherin, Anthony (2019) Stray Arts (and Other Inventions). Penteract Press

Etherin, Anthony (2021) The Utu Sonnets. Penteract Press

Gerofsky, Susan (2020) ‘Two New Combinatoric Poetry Forms:
Braided Bellringing PH4 Poems & Anagrammatic, Anglo Saxon- inspired Poems’.Bridges 2020 Conference Proceedings. Available at

Gerofsky, Susan (2021) Seven Strands of Alphabetical Braided Crows. (Film) Available at

Gerofsky, S., Knoll, E., Taylor, T. and Campbell-Cousins, A. (2018) ‘Experiencing Group Structure: Observing, Creating and Performing the Plain Hunt on 4 via Music, Poetry, Visual and Culinary Arts’. Bridges 2018 Conference Proceedings. Available at 

Growney, JoAnne: Intersections – Poetry with Mathematics. Available at

May D. (2020) ‘Poems Structured by Mathematics’ in Sriraman B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham.

Strickland, Stephanie (2020) Ringing the Changes. Denver, Counterpath

Terry, Philip (ed) (2019) The Penguin Book of Oulipo. Penguin Random House UK

Vernon, Phil (2020) Poetry After Auschwitz. London, SPM Publications

Updated on 20th August 2021. This is a summary of my former blog post on Permutations in poetry.

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