4 problems

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Nienhuis's connective-constant conjecture for the hexagonal lattice
Nienhuis's connective-constant conjecture. The connective constant of the hexagonal lattice equals
Conjecturesolvedconnective-constants lattice-models self-avoiding-walksarXiv posted 2 days ago
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The SOP connective-constant conjecture
Let $w_{2n}$ be the number of self-overlapping polygons of length $2n$ in the SOP model, counted with multiplicity factor $\mu_\gamma$ . SOP connective-constant conjecture. The limi…
Conjectureopenconnective-constants quantum-gravity random-polygonsarXiv posted 2 days ago
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Conjecture on the connective constant of universal covers of punctured hexagonal lattices
Universal-cover connective-constant conjecture. There exists $k\in\mathbb N\cup\{0\}$ for which
Conjectureopenconnective-constants hexagonal-lattice self-avoiding-walksarXiv posted 2 days ago
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Continuity of the connective constant under local convergence
Continuity conjecture. The connective constant is continuous with respect to local convergence:
Conjectureopenconnective-constants graph-theory self-avoiding-walksarXiv posted 2 days ago

Nienhuis's connective-constant conjecture for the hexagonal lattice