The sorting order on a Coxeter group
| dc.creator | Armstrong, Drew | |
| dc.date | 2007-12-07 | |
| dc.date | 2009-03-30 | |
| dc.date.accessioned | 2026-07-07T12:57:20Z | |
| dc.date.available | 2026-07-07T12:57:20Z | |
| dc.description | Let $(W,S)$ be an arbitrary Coxeter system. For each word $ω$ in the generators we define a partial order--called the {\sf $ω$-sorting order}--on the set of group elements $W_ω\subseteq W$ that occur as subwords of $ω$. We show that the $ω$-sorting order is a supersolvable join-distributive lattice and that it is strictly between the weak and Bruhat orders on the group. Moreover, the $ω$-sorting order is a "maximal lattice" in the sense that the addition of any collection of Bruhat covers results in a nonlattice. Along the way we define a class of structures called {\sf supersolvable antimatroids} and we show that these are equivalent to the class of supersolvable join-distributive lattices. | |
| dc.description | 34 pages, 7 figures. Final version, to appear in Journal of Combinatorial Theory Series A | |
| dc.identifier | https://arxiv.org/abs/0712.1047 | |
| dc.identifier | http://arxiv.org/abs/0712.1047 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224896 | |
| dc.subject | Combinatorics | |
| dc.subject | Group Theory | |
| dc.subject | 20F55; 06A07 | |
| dc.title | The sorting order on a Coxeter group | |
| dc.type | text |