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arXiv · 1704.05792

d-Complete posets: local structural axioms, properties, and equivalent definitions

Robert A. Proctor·Lindsey M. Scoppetta
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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.

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Robert A. Proctor, Lindsey M. Scoppetta. 2017-04-19. d-Complete posets: local structural axioms, properties, and equivalent definitions. https://arxiv.org/abs/1704.05792

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