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Homogeneous Length Functions on Groups: Intertwined Computer and Human Proofs

  • Siddhartha GadgilEmail author
Article
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Abstract

We describe a case of an interplay between human and computer proving which played a role in the discovery of an interesting mathematical result (Fritz et al. in Algebra Number Theory 12:1773–1786, 2018). The unusual feature of the use of computers here was that a computer generated but human readable proof was read, understood, generalized and abstracted by mathematicians to obtain the key lemma in an interesting mathematical result.

Keywords

Type theory Homotopy type theory Geometric group theory 

Mathematics Subject Classification

03B15 (primary) 20F12 20F65 (secondary) 

Notes

Acknowledgements

I thank the referees and the editors for many valuable comments, which have led to the paper being completely rewritten twice and much improved in the process. It is also a pleasure to thank the rest of the PolyMath 14 team for the collaboration of which the work described here is a part.

References

  1. 1.
    Fritz, T., Gadgil, S., Khare, A., Nielsen, P., Silberman, L., Tao, T.: Homogeneous length functions on groups. Algebra Number Theory 12, 1773–1786 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
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    Gadgil, S.: Watson–Crick pairing, the Heisenberg group and Milnor invariants. J. Math. Biol. 59, 123–142 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
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    Khare, A., Rajaratnam, B.: The Khinchin–Kahane inequality and Banach space embeddings for metric groups, preprint (2016)Google Scholar
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    Khare, A., Rajaratnam, B.: The Hoffmann–Jørgensen inequality in metric semigroups. Ann. Probab. 45, 4101–4111 (2017)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia

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