Data for verifying the LP condition for the hard-core model on the square lattice:
Here is the description of the 162-type reduced matrix Mr of M8 that avoids
cycles of length less or equal to eight.
Here are the piecewise linear functions found by the LP for each type of the above matrix M_r. This file has huge lines and is supposed to only be read by computers.
Here is the format of the file:
There are 153 lines in total. Each of the first 151 lines contains the subintervals for each NON-transient type of the above matrix. The subintevals are given as "[a,b]". The 152nd line
is a single line containing the piecewise linear functions corresponding to the subintervals. They appear in the same order as the subintervals, i.e., the first two numbers are for the coefficients of the linear function that is in
the first subinterval for type 5 (the first line of the file) and so on. The last line is the objective value of the linear program.
Here is the Maple file for verifying Lemma 5 and here is the file for Lemma 6.