Counting polycubes without the dimensionality curse

DOI10.1016/j.disc.2009.02.023zbMath1193.05054OpenAlexW2029862292MaRDI QIDQ1043990

Gill Barequet, Gadi Aleksandrowicz

Publication date: 10 December 2009

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2009.02.023

zbMATH Keywords

enumerationlattice animalssubgraph countingpolycubes

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Polyominoes (05B50)

Related Items (9)

Simulation study of random sequential deposition of binary mixtures of lattice animals on a three-dimensional cubic lattice ⋮ Parallel Enumeration of Lattice Animals ⋮ Unnamed Item ⋮ Formulae and growth rates of high-dimensional polycubes ⋮ The growth rate of high-dimensional tree polycubes ⋮ Automatic generation of formulae for polyominoes with a fixed perimeter defect ⋮ Improved upper bounds on the growth constants of polyominoes and polycubes ⋮ A new mathematical model for tiling finite regions of the plane with polyominoes ⋮ Counting \(n\)-cell polycubes proper in \(n - k\) dimensions

Uses Software

• OEIS

Cites Work

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• Counting polyominoes: yet another attack
• Counting lattice animals: A parallel attack
• A pattern theorem for lattice clusters
• Lattice animals and heaps of dimers
• On the generation and enumeration of some classes of convex polyominoes
• Reverse search for enumeration
• Formulae and Growth Rates of High-Dimensional Polycubes
• The free energy of a collapsing branched polymer
• Two-Dimensional Cluster-Correcting Codes
• Counting d-Dimensional Polycubes and Nonrectangular Planar Polyominoes
• Counting multidimensional polyominoes
• 1/d-expansions for the free energy of lattice animal models of a self-interacting branched polymer
• Cell Growth Problems
• Enumerations of lattice animals and trees

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