Abstract
Let (W, S) be an arbitrary Coxeter system. For each word ω in the generators we define a partial order-called the ω-sorting order-on the set of group elements Wω ⊆ 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 supersolvable antimatroids and we show that these are equivalent to the class of supersolvable join-distributive lattices.
Original language | English (US) |
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Pages (from-to) | 1285-1305 |
Number of pages | 21 |
Journal | Journal of Combinatorial Theory. Series A |
Volume | 116 |
Issue number | 8 |
DOIs | |
State | Published - Nov 2009 |
Externally published | Yes |
Keywords
- Abstract convex geometry
- Antimatroid
- Catalan number
- Coxeter group
- Join-distributive lattice
- Lattice
- Partial order
- Sorting algorithm
- Supersolvable lattice
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics