Sortable elements and Cambrian lattices
组合数学
2026-05-13 v1
摘要
We show that the Coxeter-sortable elements in a finite Coxeter group W are the minimal congruence-class representatives of a lattice congruence of the weak order on W. We identify this congruence as the Cambrian congruence on W, so that the Cambrian lattice is the weak order on Coxeter-sortable elements. These results exhibit W-Catalan combinatorics arising in the context of the lattice theory of the weak order on W.
引用
@article{arxiv.math/0512339,
title = {Sortable elements and Cambrian lattices},
author = {Nathan Reading},
journal= {arXiv preprint arXiv:math/0512339},
year = {2026}
}
备注
23 pages, 9 figures