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Marked tubes and the graph multiplihedron
Satyan Devadoss and Stefan Forcey
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Algebraic & Geometric Topology 8
(2008) 2081–2108
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Abstract
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Given a graph G, we construct a convex polytope whose face poset is based on
marked subgraphs of G. Dubbed the graph multiplihedron, we provide a realization
using integer coordinates. Not only does this yield a natural generalization of the
multiplihedron, but features of this polytope appear in works related to quilted disks,
bordered Riemann surfaces and operadic structures. Certain examples of graph
multiplihedra are related to Minkowski sums of simplices and cubes and others to the
permutohedron.
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Keywords
multiplihedron, graph associahedron,
realization, convex hull
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Mathematical Subject Classification
Primary: 52B11
Secondary: 18D50, 55P48
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Publication
Received: 28 July 2008
Revised: 10 October 2008
Accepted: 13 October 2008
Published: 12 November 2008
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