Capturing Polytopal Symmetries by Coloring the Edge-Graph

Abstract A (convex) polytope $$P\subset \mathbb {R}^d$$ and its edge-graph $$G_P$$ can have very distinct symmetry properties, in that the edge-graph can be much more symmetric than the polytope. In this article we ask whether this can be “rectified” by coloring the vertices and edges of $$G_P$$, th...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Winter, Martin [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Convex polytopes Linear symmetries Orthogonal symmetries Edge-graph Graph coloring Graph symmetries

Anmerkung:	© The Author(s) 2023

Übergeordnetes Werk:	Enthalten in: Discrete & computational geometry - Springer US, 1986, 71(2023), 3 vom: 27. Sept., Seite 1003-1020
Übergeordnetes Werk:	volume:71 ; year:2023 ; number:3 ; day:27 ; month:09 ; pages:1003-1020

Links:	Volltext

DOI / URN:	10.1007/s00454-023-00560-7

Katalog-ID:	SPR055098371

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520			\|a Abstract A (convex) polytope $$P\subset \mathbb {R}^d$$ and its edge-graph $$G_P$$ can have very distinct symmetry properties, in that the edge-graph can be much more symmetric than the polytope. In this article we ask whether this can be “rectified” by coloring the vertices and edges of $$G_P$$, that is, whether we can find such a coloring so that the combinatorial symmetry group of the colored edge-graph is actually isomorphic (in a natural way) to the linear or orthogonal symmetry group of the polytope. As it turns out, such colorings exist and some of them can be constructed quite naturally. However, actually proving that they “capture polytopal symmetries” involves applying rather unexpected techniques from the intersection of convex geometry and spectral graph theory.
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author_variant	m w mw
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bklnumber	31.59 31.12 31.76
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allfields	10.1007/s00454-023-00560-7 doi (DE-627)SPR055098371 (SPR)s00454-023-00560-7-e DE-627 ger DE-627 rakwb eng 510 004 VZ 510 004 VZ 31.59 bkl 31.12 bkl 31.76 bkl Winter, Martin verfasserin (orcid)0000-0002-3817-9494 aut Capturing Polytopal Symmetries by Coloring the Edge-Graph 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract A (convex) polytope $$P\subset \mathbb {R}^d$$ and its edge-graph $$G_P$$ can have very distinct symmetry properties, in that the edge-graph can be much more symmetric than the polytope. In this article we ask whether this can be “rectified” by coloring the vertices and edges of $$G_P$$, that is, whether we can find such a coloring so that the combinatorial symmetry group of the colored edge-graph is actually isomorphic (in a natural way) to the linear or orthogonal symmetry group of the polytope. As it turns out, such colorings exist and some of them can be constructed quite naturally. However, actually proving that they “capture polytopal symmetries” involves applying rather unexpected techniques from the intersection of convex geometry and spectral graph theory. Convex polytopes (dpeaa)DE-He213 Linear symmetries (dpeaa)DE-He213 Orthogonal symmetries (dpeaa)DE-He213 Edge-graph (dpeaa)DE-He213 Graph coloring (dpeaa)DE-He213 Graph symmetries (dpeaa)DE-He213 Enthalten in Discrete & computational geometry Springer US, 1986 71(2023), 3 vom: 27. Sept., Seite 1003-1020 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:71 year:2023 number:3 day:27 month:09 pages:1003-1020 https://dx.doi.org/10.1007/s00454-023-00560-7 kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.59 VZ 31.12 VZ 31.76 VZ AR 71 2023 3 27 09 1003-1020
spelling	10.1007/s00454-023-00560-7 doi (DE-627)SPR055098371 (SPR)s00454-023-00560-7-e DE-627 ger DE-627 rakwb eng 510 004 VZ 510 004 VZ 31.59 bkl 31.12 bkl 31.76 bkl Winter, Martin verfasserin (orcid)0000-0002-3817-9494 aut Capturing Polytopal Symmetries by Coloring the Edge-Graph 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract A (convex) polytope $$P\subset \mathbb {R}^d$$ and its edge-graph $$G_P$$ can have very distinct symmetry properties, in that the edge-graph can be much more symmetric than the polytope. In this article we ask whether this can be “rectified” by coloring the vertices and edges of $$G_P$$, that is, whether we can find such a coloring so that the combinatorial symmetry group of the colored edge-graph is actually isomorphic (in a natural way) to the linear or orthogonal symmetry group of the polytope. As it turns out, such colorings exist and some of them can be constructed quite naturally. However, actually proving that they “capture polytopal symmetries” involves applying rather unexpected techniques from the intersection of convex geometry and spectral graph theory. Convex polytopes (dpeaa)DE-He213 Linear symmetries (dpeaa)DE-He213 Orthogonal symmetries (dpeaa)DE-He213 Edge-graph (dpeaa)DE-He213 Graph coloring (dpeaa)DE-He213 Graph symmetries (dpeaa)DE-He213 Enthalten in Discrete & computational geometry Springer US, 1986 71(2023), 3 vom: 27. Sept., Seite 1003-1020 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:71 year:2023 number:3 day:27 month:09 pages:1003-1020 https://dx.doi.org/10.1007/s00454-023-00560-7 kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.59 VZ 31.12 VZ 31.76 VZ AR 71 2023 3 27 09 1003-1020
allfields_unstemmed	10.1007/s00454-023-00560-7 doi (DE-627)SPR055098371 (SPR)s00454-023-00560-7-e DE-627 ger DE-627 rakwb eng 510 004 VZ 510 004 VZ 31.59 bkl 31.12 bkl 31.76 bkl Winter, Martin verfasserin (orcid)0000-0002-3817-9494 aut Capturing Polytopal Symmetries by Coloring the Edge-Graph 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract A (convex) polytope $$P\subset \mathbb {R}^d$$ and its edge-graph $$G_P$$ can have very distinct symmetry properties, in that the edge-graph can be much more symmetric than the polytope. In this article we ask whether this can be “rectified” by coloring the vertices and edges of $$G_P$$, that is, whether we can find such a coloring so that the combinatorial symmetry group of the colored edge-graph is actually isomorphic (in a natural way) to the linear or orthogonal symmetry group of the polytope. As it turns out, such colorings exist and some of them can be constructed quite naturally. However, actually proving that they “capture polytopal symmetries” involves applying rather unexpected techniques from the intersection of convex geometry and spectral graph theory. Convex polytopes (dpeaa)DE-He213 Linear symmetries (dpeaa)DE-He213 Orthogonal symmetries (dpeaa)DE-He213 Edge-graph (dpeaa)DE-He213 Graph coloring (dpeaa)DE-He213 Graph symmetries (dpeaa)DE-He213 Enthalten in Discrete & computational geometry Springer US, 1986 71(2023), 3 vom: 27. Sept., Seite 1003-1020 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:71 year:2023 number:3 day:27 month:09 pages:1003-1020 https://dx.doi.org/10.1007/s00454-023-00560-7 kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.59 VZ 31.12 VZ 31.76 VZ AR 71 2023 3 27 09 1003-1020
allfieldsGer	10.1007/s00454-023-00560-7 doi (DE-627)SPR055098371 (SPR)s00454-023-00560-7-e DE-627 ger DE-627 rakwb eng 510 004 VZ 510 004 VZ 31.59 bkl 31.12 bkl 31.76 bkl Winter, Martin verfasserin (orcid)0000-0002-3817-9494 aut Capturing Polytopal Symmetries by Coloring the Edge-Graph 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract A (convex) polytope $$P\subset \mathbb {R}^d$$ and its edge-graph $$G_P$$ can have very distinct symmetry properties, in that the edge-graph can be much more symmetric than the polytope. In this article we ask whether this can be “rectified” by coloring the vertices and edges of $$G_P$$, that is, whether we can find such a coloring so that the combinatorial symmetry group of the colored edge-graph is actually isomorphic (in a natural way) to the linear or orthogonal symmetry group of the polytope. As it turns out, such colorings exist and some of them can be constructed quite naturally. However, actually proving that they “capture polytopal symmetries” involves applying rather unexpected techniques from the intersection of convex geometry and spectral graph theory. Convex polytopes (dpeaa)DE-He213 Linear symmetries (dpeaa)DE-He213 Orthogonal symmetries (dpeaa)DE-He213 Edge-graph (dpeaa)DE-He213 Graph coloring (dpeaa)DE-He213 Graph symmetries (dpeaa)DE-He213 Enthalten in Discrete & computational geometry Springer US, 1986 71(2023), 3 vom: 27. Sept., Seite 1003-1020 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:71 year:2023 number:3 day:27 month:09 pages:1003-1020 https://dx.doi.org/10.1007/s00454-023-00560-7 kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.59 VZ 31.12 VZ 31.76 VZ AR 71 2023 3 27 09 1003-1020
allfieldsSound	10.1007/s00454-023-00560-7 doi (DE-627)SPR055098371 (SPR)s00454-023-00560-7-e DE-627 ger DE-627 rakwb eng 510 004 VZ 510 004 VZ 31.59 bkl 31.12 bkl 31.76 bkl Winter, Martin verfasserin (orcid)0000-0002-3817-9494 aut Capturing Polytopal Symmetries by Coloring the Edge-Graph 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract A (convex) polytope $$P\subset \mathbb {R}^d$$ and its edge-graph $$G_P$$ can have very distinct symmetry properties, in that the edge-graph can be much more symmetric than the polytope. In this article we ask whether this can be “rectified” by coloring the vertices and edges of $$G_P$$, that is, whether we can find such a coloring so that the combinatorial symmetry group of the colored edge-graph is actually isomorphic (in a natural way) to the linear or orthogonal symmetry group of the polytope. As it turns out, such colorings exist and some of them can be constructed quite naturally. However, actually proving that they “capture polytopal symmetries” involves applying rather unexpected techniques from the intersection of convex geometry and spectral graph theory. Convex polytopes (dpeaa)DE-He213 Linear symmetries (dpeaa)DE-He213 Orthogonal symmetries (dpeaa)DE-He213 Edge-graph (dpeaa)DE-He213 Graph coloring (dpeaa)DE-He213 Graph symmetries (dpeaa)DE-He213 Enthalten in Discrete & computational geometry Springer US, 1986 71(2023), 3 vom: 27. Sept., Seite 1003-1020 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:71 year:2023 number:3 day:27 month:09 pages:1003-1020 https://dx.doi.org/10.1007/s00454-023-00560-7 kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.59 VZ 31.12 VZ 31.76 VZ AR 71 2023 3 27 09 1003-1020
language	English
source	Enthalten in Discrete & computational geometry 71(2023), 3 vom: 27. Sept., Seite 1003-1020 volume:71 year:2023 number:3 day:27 month:09 pages:1003-1020
sourceStr	Enthalten in Discrete & computational geometry 71(2023), 3 vom: 27. Sept., Seite 1003-1020 volume:71 year:2023 number:3 day:27 month:09 pages:1003-1020
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Convex polytopes Linear symmetries Orthogonal symmetries Edge-graph Graph coloring Graph symmetries
dewey-raw	510
isfreeaccess_bool	true
container_title	Discrete & computational geometry
authorswithroles_txt_mv	Winter, Martin @@aut@@
publishDateDaySort_date	2023-09-27T00:00:00Z
hierarchy_top_id	253722330
dewey-sort	3510
id	SPR055098371
language_de	englisch
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In this article we ask whether this can be “rectified” by coloring the vertices and edges of $$G_P$$, that is, whether we can find such a coloring so that the combinatorial symmetry group of the colored edge-graph is actually isomorphic (in a natural way) to the linear or orthogonal symmetry group of the polytope. As it turns out, such colorings exist and some of them can be constructed quite naturally. 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author	Winter, Martin
spellingShingle	Winter, Martin ddc 510 bkl 31.59 bkl 31.12 bkl 31.76 misc Convex polytopes misc Linear symmetries misc Orthogonal symmetries misc Edge-graph misc Graph coloring misc Graph symmetries Capturing Polytopal Symmetries by Coloring the Edge-Graph
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topic_title	510 004 VZ 31.59 bkl 31.12 bkl 31.76 bkl Capturing Polytopal Symmetries by Coloring the Edge-Graph Convex polytopes (dpeaa)DE-He213 Linear symmetries (dpeaa)DE-He213 Orthogonal symmetries (dpeaa)DE-He213 Edge-graph (dpeaa)DE-He213 Graph coloring (dpeaa)DE-He213 Graph symmetries (dpeaa)DE-He213
topic	ddc 510 bkl 31.59 bkl 31.12 bkl 31.76 misc Convex polytopes misc Linear symmetries misc Orthogonal symmetries misc Edge-graph misc Graph coloring misc Graph symmetries
topic_unstemmed	ddc 510 bkl 31.59 bkl 31.12 bkl 31.76 misc Convex polytopes misc Linear symmetries misc Orthogonal symmetries misc Edge-graph misc Graph coloring misc Graph symmetries
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title	Capturing Polytopal Symmetries by Coloring the Edge-Graph
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title_full	Capturing Polytopal Symmetries by Coloring the Edge-Graph
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title_sort	capturing polytopal symmetries by coloring the edge-graph
title_auth	Capturing Polytopal Symmetries by Coloring the Edge-Graph
abstract	Abstract A (convex) polytope $$P\subset \mathbb {R}^d$$ and its edge-graph $$G_P$$ can have very distinct symmetry properties, in that the edge-graph can be much more symmetric than the polytope. In this article we ask whether this can be “rectified” by coloring the vertices and edges of $$G_P$$, that is, whether we can find such a coloring so that the combinatorial symmetry group of the colored edge-graph is actually isomorphic (in a natural way) to the linear or orthogonal symmetry group of the polytope. As it turns out, such colorings exist and some of them can be constructed quite naturally. However, actually proving that they “capture polytopal symmetries” involves applying rather unexpected techniques from the intersection of convex geometry and spectral graph theory. © The Author(s) 2023
abstractGer	Abstract A (convex) polytope $$P\subset \mathbb {R}^d$$ and its edge-graph $$G_P$$ can have very distinct symmetry properties, in that the edge-graph can be much more symmetric than the polytope. In this article we ask whether this can be “rectified” by coloring the vertices and edges of $$G_P$$, that is, whether we can find such a coloring so that the combinatorial symmetry group of the colored edge-graph is actually isomorphic (in a natural way) to the linear or orthogonal symmetry group of the polytope. As it turns out, such colorings exist and some of them can be constructed quite naturally. However, actually proving that they “capture polytopal symmetries” involves applying rather unexpected techniques from the intersection of convex geometry and spectral graph theory. © The Author(s) 2023
abstract_unstemmed	Abstract A (convex) polytope $$P\subset \mathbb {R}^d$$ and its edge-graph $$G_P$$ can have very distinct symmetry properties, in that the edge-graph can be much more symmetric than the polytope. In this article we ask whether this can be “rectified” by coloring the vertices and edges of $$G_P$$, that is, whether we can find such a coloring so that the combinatorial symmetry group of the colored edge-graph is actually isomorphic (in a natural way) to the linear or orthogonal symmetry group of the polytope. As it turns out, such colorings exist and some of them can be constructed quite naturally. However, actually proving that they “capture polytopal symmetries” involves applying rather unexpected techniques from the intersection of convex geometry and spectral graph theory. © The Author(s) 2023
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container_issue	3
title_short	Capturing Polytopal Symmetries by Coloring the Edge-Graph
url	https://dx.doi.org/10.1007/s00454-023-00560-7
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doi_str	10.1007/s00454-023-00560-7
up_date	2024-07-04T04:09:20.422Z
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