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

  • Tomas Berggren

    KTH Royal Institute of Technology, Stockholm, Sweden; University of South Florida, Tampa, USA
    ORCID

  • Marianna Russkikh

    University of Notre Dame, USA
    ORCID
Perfect t-embeddings and the octahedron equation of the two-periodic Aztec diamond cover
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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 with appropriate flat initial conditions.

Cite this article

Tomas Berggren, Marianna Russkikh, Perfect t-embeddings and the octahedron equation of the two-periodic Aztec diamond. Ann. Inst. Henri Poincaré Comb. Phys. Interact. (2025), published online first

DOI 10.4171/AIHPD/220