Volume 8, issue 4 (2008)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Marked tubes and the graph multiplihedron

Satyan Devadoss and Stefan Forcey

Algebraic & Geometric Topology 8 (2008) 2081–2108
Abstract

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.

Keywords
multiplihedron, graph associahedron, realization, convex hull
Mathematical Subject Classification 2000
Primary: 52B11
Secondary: 18D50, 55P48
References
Publication
Received: 28 July 2008
Revised: 10 October 2008
Accepted: 13 October 2008
Published: 12 November 2008
Authors
Satyan Devadoss
Department of Mathematics and Statistics
Williams College
Williamstown, MA 01267
USA
http://www.williams.edu/mathematics/devadoss/
Stefan Forcey
Department of Physics and Mathematics
Tennessee State University
Nashville, TN 37209
USA
http://faculty.tnstate.edu/sforcey/