Formulae and growth rates of high-dimensional polycubes

DOI10.1007/s00493-010-2448-8zbMath1231.05068OpenAlexW1964063518WikidataQ56428735 ScholiaQ56428735MaRDI QIDQ555508

Gill Barequet, Günter Rote, Ronnie Barequet

Publication date: 22 July 2011

Published in: Combinatorica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00493-010-2448-8

zbMATH Keywords

spanning treepolyominoes\(d\)-dimensional polycubeedge-labeled directed treehypercubic latticeLunnon's formulaminimal proper polycube

Mathematics Subject Classification ID

Trees (05C05) Asymptotic enumeration (05A16) Polyominoes (05B50)

Related Items (15)

Automatic proofs for formulae enumerating proper polycubes ⋮ High-dimensional holeyominoes ⋮ Analyticity Results in Bernoulli Percolation ⋮ Derivation of Kubo's formula for disordered systems at zero temperature ⋮ Absolute convergence of the free energy of the BEG model in the disordered region for all temperatures ⋮ Series expansion of the percolation threshold on hypercubic lattices ⋮ Concatenation arguments and their applications to polyominoes and polycubes ⋮ Unnamed Item ⋮ The growth rate of high-dimensional tree polycubes ⋮ The Perimeter of Proper Polycubes ⋮ Expansion in High Dimension for the Growth Constants of Lattice Trees and Lattice Animals ⋮ The planar limit of \(\mathcal{N} = 2\) superconformal field theories ⋮ Polycubes with small perimeter defect ⋮ Improved upper bounds on the growth constants of polyominoes and polycubes ⋮ Counting \(n\)-cell polycubes proper in \(n - k\) dimensions

Uses Software

• OEIS

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• Cell Growth Problems
• A Procedure for Improving the Upper Bound for the Number of n-Ominoes

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