A polynomial is stored in a file on the form
"coefficient exponent1 exponent2 ...", one monomial on each row, only
non-zero monomials are stored and in no particular order. The end of a
polynomial is recognised by a monomial having coefficient zero. For
example, this is the Ising partition function for the 2x2 grid:

1 4 4

4 0 2

4 0 0

2 -4 0

4 0 -2

1 4 -4

0 0 0

and this is to be read as

x^{4}y^{4} + 4y^{2} + 4 + 2x^{-4} +
4y^{-2} + x^{4}y^{-4}

### Ising partition functions (two variables)

C_{n} x C_{n} for n=3...16
(Update 2007-06-15: n=16 added)

C_{2}xC_{2},
C_{3}xC_{3},
C_{4}xC_{4},
C_{5}xC_{5},
C_{6}xC_{6},
C_{7}xC_{7},
C_{8}xC_{8},
C_{9}xC_{9},

C_{10}xC_{10},
C_{11}xC_{11},
C_{12}xC_{12},
C_{13}xC_{13},
C_{14}xC_{14},
C_{15}xC_{15},
C_{16}xC_{16}

P_{n} x P_{n} for n=2...16

P_{n} z P_{n} (triangular) for n=2...13

P_{n} * P_{n} (strong product) for n=2...13

P_{n} x P_{n} x P_{n} for
n=2,3,4,5 (only one variable for n=5)

C_{n} x C_{n} x C_{n} for n=2,3,4

R. Häggkvist and P.H. Lundow, J. Stat. Phys. 108 (2002) 429-457.

P.H. Lundow, Research reports, No. 14 (1999), Department of mathematics,
Umeå university
(pdf).

Partition functions for C_{n} x C_{n} in one variable
for n up to 320 can be found
here , see
Phys. Rev. E 69 (2004) 046104.
### Van der Waerden polynomials (two variables)

The coefficient of x^{a} y^{b} is the number of
spanning subgraphs having a edges and b vertices of odd degree. The
coefficient for a=k and b=2k is then the number of k-matchings.

C_{n} x C_{n} for
n=3...16

P_{n} x P_{n} for
n=2...16

P_{n} z P_{n} (triangular)
for n=2...13

P_{n} * P_{n} (strong
product) for n=2...13