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  • sym_scene_analysis_REV31_10_17

    Rights statement: This is the author’s version of a work that was accepted for publication in Discrete Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete Applied Mathematics, 236, 2018 DOI: 10.1016/j.dam.2017.11.017

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Characterizing minimally flat symmetric hypergraphs

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>19/02/2018
<mark>Journal</mark>Discrete Applied Mathematics
Volume236
Number of pages14
Pages (from-to)256-269
Publication StatusPublished
Early online date6/12/17
<mark>Original language</mark>English

Abstract

In Kaszanitzky and Schulze (2017) we gave necessary conditions for a symmetric d-picture (i.e., a symmetric realization of an incidence structure in Rd) to be minimally flat, that is, to be non-liftable to a polyhedral scene without having redundant constraints. These conditions imply very simply stated restrictions on the number of those structural components of the picture that are fixed by the elements of its symmetry group. In this paper we show that these conditions on the fixed structural components, together with the standard non-symmetric counts, are also sufficient for a plane picture which is generic with three-fold rotational symmetry C3 to be minimally flat. This combinatorial characterization of minimally flat C3-generic pictures is obtained via a new inductive construction scheme for symmetric sparse hypergraphs. We also give a sufficient condition for sharpness of pictures with C3 symmetry.

Bibliographic note

This is the author’s version of a work that was accepted for publication in Discrete Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete Applied Mathematics, 236, 2018 DOI: 10.1016/j.dam.2017.11.017