




A lattice animal is a finite set of connected vertices of a regular lattice. Lattice animals on the square lattice are better known as polyominoes. On the cubic lattice they are called polycubes. The figure above shows all possible polycubes of size n = 4.
The enumeration of lattice animals is a longstanding combinatorial problem that has some motivations in physics, for example in the study of branched polymers and percolation. For most lattices we don't know a formula for the number of lattice animals of a given size n, and all we can do is to count them one by one. Since the number of lattice animals grows exponentially with n, this counting is a demanding task, even with a fast computer.
We develop fast algorithms for the enumeration of lattice animals, and we run these algorithms on parallel computers. We also work out combinatorial arguments that complement computer based enumerations.
Please check out the publications if you want to learn more about the problem and our algorithms. If you are an expert, you might want to go directly to the enumeration data or to the source code.
The coefficients G_{n} to compute the formula for the perimeter polynomials for arbitrary dimension d and fixed size n are listed in the following files:
n  2  3  4  5  6  7  8  9  10  11  12 
G_{n}  G2.dat  G3.dat  G4.dat  G5.dat  G6.dat  G7.dat  G8.dat  G9.dat  G10.dat  G11.dat  G12.dat 
e  2  3  4  5  6  7  8  9  10  11 
g_{g}  g2_bond.dat  g3_bond.dat  g4_bond.dat  g5_bond.dat  g6_bond.dat  g7_bond.dat  g8_bond.dat  g9_bond.dat  g10_bond.dat  g11_bond.dat 
The coefficients G_{e,t,v} to compute the formulas for the perimeter polynomials for arbitrary dimension d and fixed size e are listed in the following files:
e  2  3  4  5  6  7  8  9  10  11 
G_{e}  G2_bond.dat  G3_bond.dat  G4_bond.dat  G5_bond.dat  G6_bond.dat  G7_bond.dat  G8_bond.dat  G9_bond.dat  G10_bond.dat  G11_bond.dat 
cluster numbers A_{d}(n)  cluster series S_{d}  

d  data  OEIS  data  OEIS 
3  A3.dat  A001931  S3.dat  A003211 
4  A4.dat  A151830  S4.dat  
5  A5.dat  A151831  S5.dat  
6  A6.dat  A151832  S6.dat  
7  A7.dat  A151833  S7.dat  
8  A8.dat  A151834  S8.dat  
9  A9.dat  A151835  S9.dat  
10  A10.dat  S10.dat 





© by Stephan Mertens (Datenschutzerklärung)
updated on Friday, October 26th 2018, 10:06:23 CET;