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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Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Characterizing minimally flat symmetric hypergraphs. / Kaszanitzky, Viktoria Eszter; Schulze, Bernd.
In: Discrete Applied Mathematics, Vol. 236, 19.02.2018, p. 256-269.Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -