The Dimer Constant of the Cubic Lattice
Statement
The dimer constant of , the exponential growth rate of perfect matchings of the cubic lattice, has no closed form and is pinned only by bounds. The upper bound improves from Lundow's , standing since 2001, to , via diagonal transfer layers and an inequality of Csikvari relating the spectral radius of the transfer matrix to the constant.
Record
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No person has examined this. Nothing here has been checked at all. say whether it holds →
computation · #1
Qidong He, using GPT-5.6 Sol UltraThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The acknowledgement attributes the paper's two key ingredients to the model: the diagonal transfer layers, which replace the symmetry argument special to the rectangular torus, and the connection with Csikvari's inequality.
a record upper bound; the exact constant remains unknown
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