Abstract
A permutation representation of a Coxeter group W naturally defines an absolute order. This family of partial orders (which includes the absolute order on W) is introduced and studied in this paper. Conditions under which the associated rank generating polynomial divides the rank generating polynomial of the absolute order on W are investigated when W is finite. Several examples, including a symmetric group action on perfect matchings, are discussed. As an application, a well-behaved absolute order on the alternating subgroup of W is defined.
| Original language | English |
|---|---|
| Pages (from-to) | 75-98 |
| Number of pages | 24 |
| Journal | Journal of Algebraic Combinatorics |
| Volume | 39 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 2014 |
Keywords
- Absolute order
- Alternating subgroup
- Coxeter group
- Group action
- Modular element
- Perfect matching
- Rank generating polynomial
- Reflection arrangement
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics