Relative helicity and tiling twist
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- by Boris Khesin and Nicolau C. Saldanha;
- Trans. Amer. Math. Soc.
- DOI: https://doi.org/10.1090/tran/9456
- Published electronically: May 8, 2025
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Abstract:
We consider domino tilings of 3D cubiculated regions. The tilings have two invariants, flux and twist, often integer-valued, which are given in purely combinatorial terms. These invariants allow one to classify the tilings with respect to certain elementary moves, flips and trits. In this paper we present a construction associating a divergence-free vector field $\xi _{\mathbf t}$ to any domino tiling ${\mathbf t}$, such that the flux of the tiling ${\mathbf t}$ can be interpreted as the (relative) rotation class of the field $\xi _{\mathbf t}$, while the twist of ${\mathbf t}$ is proved to be the relative helicity of the field $\xi _{\mathbf t}$.References
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Bibliographic Information
- Boris Khesin
- Affiliation: Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario M5S 2E4, Canada
- MR Author ID: 238631
- ORCID: 0000-0002-6425-5032
- Email: khesin@math.toronto.edu
- Nicolau C. Saldanha
- Affiliation: Departamento de Matemática, PUC-Rio, Rua Marquês de São Vicente 225, Rio de Janeiro RJ 22451-900, Brazil
- MR Author ID: 319568
- ORCID: 0000-0002-3953-5366
- Email: saldanha@puc-rio.br
- Received by editor(s): August 8, 2024
- Received by editor(s) in revised form: February 13, 2025, and March 12, 2025
- Published electronically: May 8, 2025
- Additional Notes: The first author was partially supported by an NSERC Discovery Grant. The second author was supported by CNPq, CAPES and FAPERJ (Brazil).
- © Copyright 2025 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
- MSC (2020): Primary 05B45; Secondary 57K12, 52C22, 05C70
- DOI: https://doi.org/10.1090/tran/9456