Authors: Došen, Kosta 
Petrić, Zoran 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Shuffles and concatenations in the construction of graphs
Journal: Mathematical Structures in Computer Science
Volume: 22
Issue: 6
First page: 904
Last page: 930
Issue Date: 1-Dec-2012
Rank: M22
ISSN: 0960-1295
DOI: 10.1017/S0960129511000648
This paper reports on an investigation into the role of shuffling and concatenation in the theory of graph drawing. A simple syntactic description of these and related operations is proved to be complete in the context of finite partial orders, and as general as possible. An explanation based on this result is given for a previously investigated collapse of the permutohedron into the associahedron, and for collapses into other less familiar polyhedra, including the cyclohedron. Such polyhedra have been considered recently in connection with the notion of tubing, which is closely related to tree-like finite partial orders, which are defined simply here and investigated in detail. Like the associahedron, some of these other polyhedra are involved in categorial coherence questions, which will be treated elsewhere.
Publisher: Cambridge University Press
Project: Ministry of Science of Serbia (Grants 144013 and 144029)

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