The Perimeter of Proper Polycubes

zbMath1384.05069arXiv1705.03688MaRDI QIDQ4637099

Sebastian Luther, Stephan Mertens

Publication date: 18 April 2018

Full work available at URL: https://arxiv.org/abs/1705.03688

zbMATH Keywords

percolationpolyominolattice animalperimeter polynomial

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Enumeration in graph theory (05C30) Percolation (82B43) Asymptotic enumeration (05A16) Polyominoes (05B50)

Related Items (2)

Series expansion of the percolation threshold on hypercubic lattices ⋮ Polycubes with small perimeter defect

Uses Software

• OEIS

Cites Work

• Formulae and growth rates of high-dimensional polycubes
• Polygons, polyominoes and polycubes
• Counting two-graphs related to trees
• Enumerating polyominoes with fixed perimeter defect
• Counting \(n\)-cell polycubes proper in \(n - k\) dimensions
• Some Cluster Size and Percolation Problems
• Counting multidimensional polyominoes
• Fast algorithms for genegrating integer partitions
• Pascal's Matrices
• Generating Edge-Labeled Trees
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