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A 6-Letter ‘DNA’ for Baskets with Handles

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  • James Mallos

    (Sculptor, Washington, DC 20002, USA)

Abstract

Fabric surfaces, made using techniques such as crochet and net-making, are typically worked in a linear order that meanders, without crossing itself, to ultimately visit and build the entire surface. For a closed basket, whose surface is a topological sphere, it is known that the construction can be described by a codeword on a 4-letter alphabet via Mullin’s encoding of plane graphs. Mullin’s code exemplifies the formal language known as the Shuffled Dyck Language with 2 Types of Parenthesis ( S D L 2 ). Besides its 4-letter alphabet, S D L 2 has some other similarities to DNA: Any word can be ‘evolved’ via a sequence of local mutations (rewriting rules), and ‘gene-splicing’ two S D L 2 words, by an insertion or concatenation, produces another S D L 2 word. However, S D L 2 comes up short when we attempt to make a basket with handles. I show that extending the language to S D L 3 , by addition of a third type of parenthesis, succeeds for orientable surfaces with handles—provided an appropriate choice of cut graph is made.

Suggested Citation

  • James Mallos, 2019. "A 6-Letter ‘DNA’ for Baskets with Handles," Mathematics, MDPI, vol. 7(2), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:165-:d:205512
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    References listed on IDEAS

    as
    1. Erik Benson & Abdulmelik Mohammed & Johan Gardell & Sergej Masich & Eugen Czeizler & Pekka Orponen & Björn Högberg, 2015. "DNA rendering of polyhedral meshes at the nanoscale," Nature, Nature, vol. 523(7561), pages 441-444, July.
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