This is a (slightly modified) copy of Fokko du Cloux's web page for the coxeter software. The version of the software is the same as that found on Fokko's home page It also includes Fokko's positivity and an enhanced 64 bit version of the software (updated 10/19/2010).



Coxeter is a computer program for the study of combinatorial aspects of Coxeter group theory, particularly those related to the Bruhat ordering and Kazhdan-Lusztig polynomials. It is written in C++, and should run on the main types of workstation under linux or unix. The current version is now version 3.0, which is now available for beta testing.

The main capabilities of the program are the following :

The program doesn't have very much in common anymore with version 1, which has been in existence for many years. The main differences, from the user's viewpoint, are the following:

Positivity: Also included is software for checking non-negativity of the structure constants of the Hecke algebra in the Kazhdan-Lusztig basis. The main thrust is to do this verification in type H4. See the README file included in the distribution, and the paper Some positivity properties for the Hecke algebra in type H4. (J. Algebra 303 (2006), no. 2, 731--741).

Download the positivity software (a gzipped tar file).

Coxeter 64 is a version of the coxeter software designed to take advantage of 64 bit architecture. The coefficients of Kazhdan-Luszztig polynomials are 32 bit unisgned untegers, and the memory management has been improved for 64 bits.

Download coxeter 64 (tar file)

The author would like to stress that Coxeter was written primarily with his own research interests in mind, and that it is made available without any promise of technical or other assistance, nor of further development. It is distributed under the copyleft license of the Free Software Foundation; therefore it is not in the public domain, but may be freely copied, distributed, modified, and incorporated into other software, provided only that the modified versions be clearly identified as such, and that programs incorporating all or part of this code be in turn distributed under the copyleft license.