Shuffles and Concatenations in Constructing of Graphs

Details Shuffles and Concatenations in Constructing of Graphs Shuffles and Concatenations in Constructing of Graphs

2010-02-18

arxiv.org/abs/1002.3577v7

Mathematics

Logic

25 pages, updated references

Scientific paper

This is an investigation of the role of shuffling and concatenating in the theory of graph drawing. A simple syntactic description of these and related operations is proved complete in the context of finite partial orders, as general as possible. An explanation based on that 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 defined simply and investigated here in detail. Like the associahedron, some of these other polyhedra are involved in categorial coherence questions, which will be treated in a sequel to this paper.

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