Discrete Mathematics & Theoretical Computer Science 
Let $(W,S)$ be an arbitrary Coxeter system. For each sequence $\omega =(\omega_1,\omega_2,\ldots) \in S^{\ast}$ in the generators we define a partial order― called the $\omega \mathsf{sorting order}$ ―on the set of group elements $W_{\omega} \subseteq W$ that occur as finite subwords of $\omega$ . We show that the $\omega$sorting order is a supersolvable joindistributive lattice and that it is strictly between the weak and strong Bruhat orders on the group. Moreover, the $\omega$sorting order is a "maximal lattice'' in the sense that the addition of any collection of edges from the Bruhat order results in a nonlattice. Along the way we define a class of structures called $\mathsf{supersolvable}$ $\mathsf{antimatroids}$ and we show that these are equivalent to the class of supersolvable joindistributive lattices.
Source : ScholeXplorer
IsRelatedTo ARXIV 2006.09321 Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.aam.2020.102129 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.2006.09321
