# Phase Coexistence and Slow Mixing for the Hard-Core Model on Z^2

## Data on taxi walks

This page links to data sets used in the papers *Phase Coexistence and Slow Mixing for the Hard-Core Model on Z^2* by A. Blanca, D. Galvin, D. Randall and P. Tetali (available here) and *Phase Coexistence for the Hard-Core Model on Z^2* by A. Blanca, E. Chen, D. Galvin, D. Randall and P. Tetali (appearing here soon).

- Enumeration of taxi walks of length
*n*, for *n* up to 60: here. (The first column is *n*, and the second column is number of taxi walks of length *n*.)
- Enumeration of bridges of length
*n*, for *n* up to 60: here. (The first column is *n*, and the second column is number of bridges of length *n*.)
- Enumeration (via Mathematica) of irreducible bridges of length
*n*, for *n* up to 60: here. (The coefficient of *x^n* in Out[96] is the number of irreducible bridges of length *n*.)
- The matrix
*A(20,60)*: here. (**Warning**: 533MB file. Both the rows and columns are indexed by equivalence classes of walks of length 20, where two walks are equilvalent if either they are the same walk or the reflection across the line *x=y* maps one to the other; the *ij* entry of the matrix counts the number of walks of length 60 that start with something in the *i*th class and end with something in the *j*th class. There are 20114 walks of length 20, and each equivalence class has size 2, so there matrix is square with dimension 10057.)
- Exhaustive list of taxi polygons of length at most 48: here. (
**Warning**: 1.14GB file. There are 8,009,144 such polygons.)
- Code used to generate taxi polygons and to implement the Goulden-Jackson cluster method: here. (Appendix A.1 gives the Goulden-Jackson Python script and Appendix A.2 gives the Python code used to list taxi polygons.) This document also contains a detailed discussion of the construction of irreducible bridges alluded to at the end of Section 4 of
*Phase Coexistence for the Hard-Core Model on Z^2*.