2024/07/10 by Nicolaides, Robert, Rowley, Peter
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2407.07881
The deletion order of a finitely generated Coxeter group W is a total order on the elements which, as is proved, is a refinement of the Bruhat order. This order is applied in [8] to construct Elnitsky tilings for any finite Coxeter group. Employing the deletion order, a corresponding normal form of an element w of W is defined which is shown to be the same as the normal form of w using right to left lexicographic ordering. Further results on the deletion order are obtained relating to the property of being Artinian and, when W is finite, its interplay with the longest element of W.