Coxeter 1

Coxeter is a computer program for the study of combinatorial questions about Coxeter groups, in particular those related to Bruhat order and Kazhdan-Lusztig polynomials. It is written in C, and should run without problems on any workstation under unix or linux. This page is now of historical interest only; the current version of Coxeter is version 3.0. Version 1.01 will compute all Kazhdan-Lusztig polynomials in all finite Coxeter groups of rank at most six, and for type A7.

The author would like to stress that Coxeter is developed primarily with his own research goals in mind, and that no promises are made regarding further developments or technical assistance of any kind. It is distributed under the GNU copyleft General Public Licence instated by the Free Software Foundation; it is therefore not in the public domain, but may be freely copied, distributed, modified, and incorporated in other programs, provided only that the modified versions be clearly identified as such, and that any software incorporating all or part of this code be also distributed under the GPL licence.


The implementation of finite Coxeter groups used in version 1.01 used in the program is based on a cascade of small transducers (see the article Fokko du Cloux, A transducer approach to Coxeter groups, J. of Symbolic Computation 27 (1999), pp. 1-14.) An ascii file containing these transducers for the exceptional groups and for small rank clasical groups is available here.