Relative Helicity and Tiling Twist
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909536480133120 |
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| author | Khesin, Boris Saldanha, Nicolau C. |
| author_facet | Khesin, Boris Saldanha, Nicolau C. |
| contents | 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 $ξ_t$ to any domino tiling $t$, such that the flux of the tiling $t$ can be interpreted as the (relative) rotation class of the field $ξ_t$, while the twist of $t$ is proved to be the relative helicity of the field $ξ_t$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_00522 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative Helicity and Tiling Twist Khesin, Boris Saldanha, Nicolau C. Combinatorics Dynamical Systems Primary 05B45, Secondary 57K12, 52C22, 05C70 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 $ξ_t$ to any domino tiling $t$, such that the flux of the tiling $t$ can be interpreted as the (relative) rotation class of the field $ξ_t$, while the twist of $t$ is proved to be the relative helicity of the field $ξ_t$. |
| title | Relative Helicity and Tiling Twist |
| topic | Combinatorics Dynamical Systems Primary 05B45, Secondary 57K12, 52C22, 05C70 |
| url | https://arxiv.org/abs/2408.00522 |