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
x4y4 + 4y2 + 4 + 2x-4 + 4y-2 + x4y-4

Ising partition functions (two variables)

Cn x Cn for n=3...16 (Update 2007-06-15: n=16 added)
      C2xC2, C3xC3, C4xC4, C5xC5, C6xC6, C7xC7, C8xC8, C9xC9,
      C10xC10, C11xC11, C12xC12, C13xC13, C14xC14, C15xC15, C16xC16
Pn x Pn for n=2...16
Pn z Pn (triangular) for n=2...13
Pn * Pn (strong product) for n=2...13
Pn x Pn x Pn for n=2,3,4,5 (only one variable for n=5)
Cn x Cn x Cn 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 Cn x Cn 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 xa yb 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.
Cn x Cn for n=3...16
Pn x Pn for n=2...16
Pn z Pn (triangular) for n=2...13
Pn * Pn (strong product) for n=2...13