Clusters, Coxeter-sortable elements and noncrossing partitions
Combinatorics
2026-05-13 v2
Abstract
We introduce Coxeter-sortable elements of a Coxeter group W. For finite W, we give bijective proofs that Coxeter-sortable elements are equinumerous with clusters and with noncrossing partitions. We characterize Coxeter-sortable elements in terms of their inversion sets and, in the classical cases, in terms of permutations.
Cite
@article{arxiv.math/0507186,
title = {Clusters, Coxeter-sortable elements and noncrossing partitions},
author = {Nathan Reading},
journal= {arXiv preprint arXiv:math/0507186},
year = {2026}
}
Comments
Minor changes in exposition, including: More precise statement in Remark 6.8; Added Remark 6.9, an observation which is helpful in the sequel (math.CO/0512339); Updated textual references to the sequel and to a paper in preparation (with D. Speyer). 28 pages, 8 figures