Claims

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1964_08_01_kesten: Kesten's 1964 theorem expands the connective constant of the k-dimensional lattice as 2k - 1 - 1/(2k) + O(1/k^2); the first terms of the asymptotics of C_k, determining no C_k; refereed, credited by the site under [Ke63].

1993_06_01_alm: Alm's 1993 paper bounds the connective constant of a lattice above by the largest eigenvalue of a matrix built from short walks, giving C_2 <= 2.696 for the square lattice; refereed, credited by the site, determining no C_k.

1993_08_07_conway_guttmann: Conway and Guttmann's 1993 paper proves the lower bound C_2 >= 2.62 for the connective constant of the square lattice by enumerating irreducible bridges up to 40 steps; refereed, credited by the site, determining no C_k.

2007_08_21_clisby_liang_slade: Clisby, Liang and Slade's 2007 paper extends the expansion of C_k in powers of 1/(2k) through order (2k)^{-11} with a remainder O((2k)^{-12}), an error estimate the paper calls rigorous; its numerical estimates are not claimed.

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