A Dynkin diagram classification theorem arising from a combinatorial problem
type: Item
instance of: scholarly article
title: A Dynkin diagram classification theorem arising from a combinatorial problem
zbMATH Open document ID: 0639.06006
DOI: 10.1016/0001-8708(86)90095-2
author: Robert A. Proctor
published in: Advances in Mathematics
publication date: 1986-01-01T00:00:00Z
review text: A poset P is vertex-labelable if there exists a rational-valued function \(\pi\) on P such that, for every order ideal \(I\subseteq P\), we have \[ \sum_{x\quad \max imal\quad in\quad I}\pi (x)-| I| =\sum_{y\quad \min imal\quad in\quad P-I}\pi (y)-| P-I|. \] The poset of all order ideals in a vertex-labelable poset is rank symmetric, rank unimodal and strongly Sperner. The author presents a complete classification of vertex-labelable posets.
Mathematics Subject Classification ID: 06D05
Mathematics Subject Classification ID: 06B15
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 4041977
zbMATH Keywords: ranked posets
zbMATH Keywords: strongly Sperner posets
zbMATH Keywords: Dynkin diagrams
zbMATH Keywords: order ideals
zbMATH Keywords: vertex-labelable poset
zbMATH Keywords: rank symmetric
zbMATH Keywords: rank unimodal
reviewed by: Mirko Navara
MaRDI profile type: Publication
full work available at URL: 0001-8708(86)90095-2
OpenAlex ID: W2054476555
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description: scientific article; zbMATH DE number 4041977