2024/08/01 by Boris Khesin, Khesin, Boris, Nicolau C. Saldanha +1 · 1 citation
Materials Science · #05C70 #52C22 #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 05B45 #Quasicrystal Structures and Properties #Secondary 57K12
paper · pdf · doi:10.48550/arxiv.2408.00522
openalex publication_date 2024/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ξt to any domino tiling t, such that the flux of the tiling t can be interpreted as the (relative) rotation class of the field ξt, while the twist of t is proved to be the relative helicity of the field ξt.