New upper bounds are proven for the growth constants λ_d of d-dimensional polycubes: λ_2 ≤ 4.5252, λ_d ≤ (2d-2)e + o(1), and λ_3 ≤ 9.3835 via iterative refinement.
15 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ L2∗L1 L4∗L1 Figure 10: The only two twigs with two dead cells and no open cells
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Improved Upper Bounds on the Growth Constants of Polyominoes and Polycubes
New upper bounds are proven for the growth constants λ_d of d-dimensional polycubes: λ_2 ≤ 4.5252, λ_d ≤ (2d-2)e + o(1), and λ_3 ≤ 9.3835 via iterative refinement.