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    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

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Characterizing minimally flat symmetric hypergraphs. / Kaszanitzky, Viktoria Eszter; Schulze, Bernd.
In: Discrete Applied Mathematics, Vol. 236, 19.02.2018, p. 256-269.

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Kaszanitzky VE, Schulze B. Characterizing minimally flat symmetric hypergraphs. Discrete Applied Mathematics. 2018 Feb 19;236:256-269. Epub 2017 Dec 6. doi: 10.1016/j.dam.2017.11.017

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Kaszanitzky, Viktoria Eszter ; Schulze, Bernd. / Characterizing minimally flat symmetric hypergraphs. In: Discrete Applied Mathematics. 2018 ; Vol. 236. pp. 256-269.

Bibtex

@article{86ff1fa0ca854dfa9b82c6ba7da85b6e,
title = "Characterizing minimally flat symmetric hypergraphs",
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.",
keywords = "Incidence structure, Picture, Polyhedral scene, Lifting, Symmetry, Sparse hypergraph",
author = "Kaszanitzky, {Viktoria Eszter} and Bernd Schulze",
note = "This is the author{\textquoteright}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",
year = "2018",
month = feb,
day = "19",
doi = "10.1016/j.dam.2017.11.017",
language = "English",
volume = "236",
pages = "256--269",
journal = "Discrete Applied Mathematics",
issn = "0166-218X",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Characterizing minimally flat symmetric hypergraphs

AU - Kaszanitzky, Viktoria Eszter

AU - Schulze, Bernd

N1 - 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

PY - 2018/2/19

Y1 - 2018/2/19

N2 - 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.

AB - 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.

KW - Incidence structure

KW - Picture

KW - Polyhedral scene

KW - Lifting

KW - Symmetry

KW - Sparse hypergraph

U2 - 10.1016/j.dam.2017.11.017

DO - 10.1016/j.dam.2017.11.017

M3 - Journal article

VL - 236

SP - 256

EP - 269

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -