Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Relative helicity and tiling twist
HTML articles powered by AMS MathViewer

by Boris Khesin and Nicolau C. Saldanha;
Trans. Amer. Math. Soc.
DOI: https://doi.org/10.1090/tran/9456
Published electronically: May 8, 2025

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
Similar Articles
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