d-Complete posets: local structural axioms, properties, and equivalent definitions
Abstract
Although d-complete posets arose along the interface between algebraic combinatorics and Lie theory, they are defined using only requirements on their local structure. These posets are a mutual generalization of rooted trees, shapes, and shifted shapes. They possess Stanley's hook product property for their P-partition generating functions and Schutzenberger's well defined jeu de taquin rectification property. The original definition of d-complete poset was lengthy, but more succinct definitions were later developed. Here several definitions are shown to be equivalent. The basic properties of d-complete posets are summarized. Background and a partial bibliography for these posets is given.
Cite
@article{arxiv.1704.05792,
title = {d-Complete posets: local structural axioms, properties, and equivalent definitions},
author = {Robert A. Proctor and Lindsey M. Scoppetta},
journal= {arXiv preprint arXiv:1704.05792},
year = {2018}
}
Comments
26 pages, 5 figures. On the question of how to define the notion of "d-complete" for infinite posets: A sentence on p. 6 is reworded, the last sentence on p. 16 is deleted, and an Added Note is inserted. References [KiYo] and [NrOk] are new. This is the final uncopyrighted version; the 'Order' journal version will also include several small exposition clarifications from the referee