Computing Joins in the Weak Order of Type B Coxeter Groups: an Algorithmic Approach

Key Points

• The aim is to develop an algorithm for computing joins in the weak order of type B Coxeter groups, specifically for signed permutations.
• Presenting an algorithm to compute joins of two elements
• Extending Markowsky's algorithm to signed permutations
• Verifying a conjecture by Dyer on geometric interpretations
• The new algorithm successfully computes joins for signed permutations
• Confirms Dyer's conjecture regarding geometric interpretations of these joins