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Oct 12 at 16:53 comment added tmh I'm not sure about $\mathbb{Z}^2$ specifically, but inequalities of this form are certainly not known to hold on $\mathbb{Z}^d$. Inequalities like this were probably the key motivation behind Kastelyn's recently disproven "bunkbed conjecture", see the introduction to arxiv.org/abs/2110.00282.
Oct 12 at 5:54 history asked Rixinner CC BY-SA 4.0