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Perfect t-embeddings and the octahedron equation of the two-periodic Aztec diamond

Published 8 Aug 2025 in math-ph, math.CO, math.MP, and math.PR | (2508.06697v1)

Abstract: This paper explores the connection between perfect t-embeddings and the octahedron equation in the setting of the two-periodic Aztec diamond. In particular, we show that the positions of both the t-embedding and the corresponding origami map can be expressed as sums of density functions arising from solutions to the octahedron equation defined on the two-periodic Aztec diamond.

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