Colorful Helly-type theorems for the volume of intersections of convex bodies

We prove the following Helly-type result. Let C 1 , … ,...
Ausführliche Beschreibung

We prove the following Helly-type result. Let C 1 , … , C 3 d be finite families of convex bodies in R d . Assume that for any colorful selection of 2d sets, C i k ∈ C i k for each 1 ≤ k ≤ 2 d with 1 ≤ i 1 < … < i 2 d ≤ 3 d , the intersection ⋂ k = 1 2 d C i k is of volume at least 1. Then there is an 1 ≤ i ≤ 3 d such that ⋂ C ∈ C i C is of volume at least d − O ( d 2 ) . Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Damásdi, Gábor [verfasserIn] Földvári, Viktória [verfasserIn] Naszódi, Márton [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	Intersection of convex sets Volume of convex bodies Colorful Helly theorem Ellipsoid Volume of intersection

Übergeordnetes Werk:	Enthalten in: Journal of combinatorial theory / A - Amsterdam [u.a.] : Elsevier, 1971, 178
Übergeordnetes Werk:	volume:178

DOI / URN:	10.1016/j.jcta.2020.105361

Katalog-ID:	ELV005088615

Internformat


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100	1		\|a Damásdi, Gábor \|e verfasserin \|0 (orcid)0000-0002-6390-5419 \|4 aut
245	1	0	\|a Colorful Helly-type theorems for the volume of intersections of convex bodies
264		1	\|c 2020
336			\|a nicht spezifiziert \|b zzz \|2 rdacontent
337			\|a Computermedien \|b c \|2 rdamedia
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520			\|a We prove the following Helly-type result. Let C 1 , … , C 3 d be finite families of convex bodies in R d . Assume that for any colorful selection of 2d sets, C i k ∈ C i k for each 1 ≤ k ≤ 2 d with 1 ≤ i 1 < … < i 2 d ≤ 3 d , the intersection ⋂ k = 1 2 d C i k is of volume at least 1. Then there is an 1 ≤ i ≤ 3 d such that ⋂ C ∈ C i C is of volume at least d − O ( d 2 ) .
650		4	\|a Intersection of convex sets
650		4	\|a Volume of convex bodies
650		4	\|a Colorful Helly theorem
650		4	\|a Ellipsoid
650		4	\|a Volume of intersection
700	1		\|a Földvári, Viktória \|e verfasserin \|0 (orcid)0000-0003-2693-0436 \|4 aut
700	1		\|a Naszódi, Márton \|e verfasserin \|0 (orcid)0000-0002-4194-0205 \|4 aut
773	0	8	\|i Enthalten in \|t Journal of combinatorial theory / A \|d Amsterdam [u.a.] : Elsevier, 1971 \|g 178 \|h Online-Ressource \|w (DE-627)266892361 \|w (DE-600)1469152-8 \|w (DE-576)104193808 \|7 nnns
773	1	8	\|g volume:178
912			\|a GBV_USEFLAG_U
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912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
936	b	k	\|a 31.12 \|j Kombinatorik \|j Graphentheorie
951			\|a AR
952			\|d 178

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bklnumber	31.12
publishDate	2020
allfields	10.1016/j.jcta.2020.105361 doi (DE-627)ELV005088615 (ELSEVIER)S0097-3165(20)30153-9 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl Damásdi, Gábor verfasserin (orcid)0000-0002-6390-5419 aut Colorful Helly-type theorems for the volume of intersections of convex bodies 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We prove the following Helly-type result. Let C 1 , … , C 3 d be finite families of convex bodies in R d . Assume that for any colorful selection of 2d sets, C i k ∈ C i k for each 1 ≤ k ≤ 2 d with 1 ≤ i 1 < … < i 2 d ≤ 3 d , the intersection ⋂ k = 1 2 d C i k is of volume at least 1. Then there is an 1 ≤ i ≤ 3 d such that ⋂ C ∈ C i C is of volume at least d − O ( d 2 ) . Intersection of convex sets Volume of convex bodies Colorful Helly theorem Ellipsoid Volume of intersection Földvári, Viktória verfasserin (orcid)0000-0003-2693-0436 aut Naszódi, Márton verfasserin (orcid)0000-0002-4194-0205 aut Enthalten in Journal of combinatorial theory / A Amsterdam [u.a.] : Elsevier, 1971 178 Online-Ressource (DE-627)266892361 (DE-600)1469152-8 (DE-576)104193808 nnns volume:178 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie AR 178
spelling	10.1016/j.jcta.2020.105361 doi (DE-627)ELV005088615 (ELSEVIER)S0097-3165(20)30153-9 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl Damásdi, Gábor verfasserin (orcid)0000-0002-6390-5419 aut Colorful Helly-type theorems for the volume of intersections of convex bodies 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We prove the following Helly-type result. Let C 1 , … , C 3 d be finite families of convex bodies in R d . Assume that for any colorful selection of 2d sets, C i k ∈ C i k for each 1 ≤ k ≤ 2 d with 1 ≤ i 1 < … < i 2 d ≤ 3 d , the intersection ⋂ k = 1 2 d C i k is of volume at least 1. Then there is an 1 ≤ i ≤ 3 d such that ⋂ C ∈ C i C is of volume at least d − O ( d 2 ) . Intersection of convex sets Volume of convex bodies Colorful Helly theorem Ellipsoid Volume of intersection Földvári, Viktória verfasserin (orcid)0000-0003-2693-0436 aut Naszódi, Márton verfasserin (orcid)0000-0002-4194-0205 aut Enthalten in Journal of combinatorial theory / A Amsterdam [u.a.] : Elsevier, 1971 178 Online-Ressource (DE-627)266892361 (DE-600)1469152-8 (DE-576)104193808 nnns volume:178 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie AR 178
allfields_unstemmed	10.1016/j.jcta.2020.105361 doi (DE-627)ELV005088615 (ELSEVIER)S0097-3165(20)30153-9 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl Damásdi, Gábor verfasserin (orcid)0000-0002-6390-5419 aut Colorful Helly-type theorems for the volume of intersections of convex bodies 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We prove the following Helly-type result. Let C 1 , … , C 3 d be finite families of convex bodies in R d . Assume that for any colorful selection of 2d sets, C i k ∈ C i k for each 1 ≤ k ≤ 2 d with 1 ≤ i 1 < … < i 2 d ≤ 3 d , the intersection ⋂ k = 1 2 d C i k is of volume at least 1. Then there is an 1 ≤ i ≤ 3 d such that ⋂ C ∈ C i C is of volume at least d − O ( d 2 ) . Intersection of convex sets Volume of convex bodies Colorful Helly theorem Ellipsoid Volume of intersection Földvári, Viktória verfasserin (orcid)0000-0003-2693-0436 aut Naszódi, Márton verfasserin (orcid)0000-0002-4194-0205 aut Enthalten in Journal of combinatorial theory / A Amsterdam [u.a.] : Elsevier, 1971 178 Online-Ressource (DE-627)266892361 (DE-600)1469152-8 (DE-576)104193808 nnns volume:178 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie AR 178
allfieldsGer	10.1016/j.jcta.2020.105361 doi (DE-627)ELV005088615 (ELSEVIER)S0097-3165(20)30153-9 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl Damásdi, Gábor verfasserin (orcid)0000-0002-6390-5419 aut Colorful Helly-type theorems for the volume of intersections of convex bodies 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We prove the following Helly-type result. Let C 1 , … , C 3 d be finite families of convex bodies in R d . Assume that for any colorful selection of 2d sets, C i k ∈ C i k for each 1 ≤ k ≤ 2 d with 1 ≤ i 1 < … < i 2 d ≤ 3 d , the intersection ⋂ k = 1 2 d C i k is of volume at least 1. Then there is an 1 ≤ i ≤ 3 d such that ⋂ C ∈ C i C is of volume at least d − O ( d 2 ) . Intersection of convex sets Volume of convex bodies Colorful Helly theorem Ellipsoid Volume of intersection Földvári, Viktória verfasserin (orcid)0000-0003-2693-0436 aut Naszódi, Márton verfasserin (orcid)0000-0002-4194-0205 aut Enthalten in Journal of combinatorial theory / A Amsterdam [u.a.] : Elsevier, 1971 178 Online-Ressource (DE-627)266892361 (DE-600)1469152-8 (DE-576)104193808 nnns volume:178 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie AR 178
allfieldsSound	10.1016/j.jcta.2020.105361 doi (DE-627)ELV005088615 (ELSEVIER)S0097-3165(20)30153-9 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl Damásdi, Gábor verfasserin (orcid)0000-0002-6390-5419 aut Colorful Helly-type theorems for the volume of intersections of convex bodies 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We prove the following Helly-type result. Let C 1 , … , C 3 d be finite families of convex bodies in R d . Assume that for any colorful selection of 2d sets, C i k ∈ C i k for each 1 ≤ k ≤ 2 d with 1 ≤ i 1 < … < i 2 d ≤ 3 d , the intersection ⋂ k = 1 2 d C i k is of volume at least 1. Then there is an 1 ≤ i ≤ 3 d such that ⋂ C ∈ C i C is of volume at least d − O ( d 2 ) . Intersection of convex sets Volume of convex bodies Colorful Helly theorem Ellipsoid Volume of intersection Földvári, Viktória verfasserin (orcid)0000-0003-2693-0436 aut Naszódi, Márton verfasserin (orcid)0000-0002-4194-0205 aut Enthalten in Journal of combinatorial theory / A Amsterdam [u.a.] : Elsevier, 1971 178 Online-Ressource (DE-627)266892361 (DE-600)1469152-8 (DE-576)104193808 nnns volume:178 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie AR 178
language	English
source	Enthalten in Journal of combinatorial theory / A 178 volume:178
sourceStr	Enthalten in Journal of combinatorial theory / A 178 volume:178
format_phy_str_mv	Article
bklname	Kombinatorik Graphentheorie
institution	findex.gbv.de
topic_facet	Intersection of convex sets Volume of convex bodies Colorful Helly theorem Ellipsoid Volume of intersection
dewey-raw	510
isfreeaccess_bool	false
container_title	Journal of combinatorial theory / A
authorswithroles_txt_mv	Damásdi, Gábor @@aut@@ Földvári, Viktória @@aut@@ Naszódi, Márton @@aut@@
publishDateDaySort_date	2020-01-01T00:00:00Z
hierarchy_top_id	266892361
dewey-sort	3510
id	ELV005088615
language_de	englisch
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author	Damásdi, Gábor
spellingShingle	Damásdi, Gábor ddc 510 bkl 31.12 misc Intersection of convex sets misc Volume of convex bodies misc Colorful Helly theorem misc Ellipsoid misc Volume of intersection Colorful Helly-type theorems for the volume of intersections of convex bodies
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topic_title	510 DE-600 31.12 bkl Colorful Helly-type theorems for the volume of intersections of convex bodies Intersection of convex sets Volume of convex bodies Colorful Helly theorem Ellipsoid Volume of intersection
topic	ddc 510 bkl 31.12 misc Intersection of convex sets misc Volume of convex bodies misc Colorful Helly theorem misc Ellipsoid misc Volume of intersection
topic_unstemmed	ddc 510 bkl 31.12 misc Intersection of convex sets misc Volume of convex bodies misc Colorful Helly theorem misc Ellipsoid misc Volume of intersection
topic_browse	ddc 510 bkl 31.12 misc Intersection of convex sets misc Volume of convex bodies misc Colorful Helly theorem misc Ellipsoid misc Volume of intersection
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title	Colorful Helly-type theorems for the volume of intersections of convex bodies
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title_full	Colorful Helly-type theorems for the volume of intersections of convex bodies
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author_browse	Damásdi, Gábor Földvári, Viktória Naszódi, Márton
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title_sort	colorful helly-type theorems for the volume of intersections of convex bodies
title_auth	Colorful Helly-type theorems for the volume of intersections of convex bodies
abstract	We prove the following Helly-type result. Let C 1 , … , C 3 d be finite families of convex bodies in R d . Assume that for any colorful selection of 2d sets, C i k ∈ C i k for each 1 ≤ k ≤ 2 d with 1 ≤ i 1 < … < i 2 d ≤ 3 d , the intersection ⋂ k = 1 2 d C i k is of volume at least 1. Then there is an 1 ≤ i ≤ 3 d such that ⋂ C ∈ C i C is of volume at least d − O ( d 2 ) .
abstractGer	We prove the following Helly-type result. Let C 1 , … , C 3 d be finite families of convex bodies in R d . Assume that for any colorful selection of 2d sets, C i k ∈ C i k for each 1 ≤ k ≤ 2 d with 1 ≤ i 1 < … < i 2 d ≤ 3 d , the intersection ⋂ k = 1 2 d C i k is of volume at least 1. Then there is an 1 ≤ i ≤ 3 d such that ⋂ C ∈ C i C is of volume at least d − O ( d 2 ) .
abstract_unstemmed	We prove the following Helly-type result. Let C 1 , … , C 3 d be finite families of convex bodies in R d . Assume that for any colorful selection of 2d sets, C i k ∈ C i k for each 1 ≤ k ≤ 2 d with 1 ≤ i 1 < … < i 2 d ≤ 3 d , the intersection ⋂ k = 1 2 d C i k is of volume at least 1. Then there is an 1 ≤ i ≤ 3 d such that ⋂ C ∈ C i C is of volume at least d − O ( d 2 ) .
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title_short	Colorful Helly-type theorems for the volume of intersections of convex bodies
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author2	Földvári, Viktória Naszódi, Márton
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doi_str	10.1016/j.jcta.2020.105361
up_date	2024-07-06T16:46:56.896Z
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score	7.401681

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Colorful Helly-type theorems for the volume of intersections of convex bodies

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Zugang & Verfügbarkeit

Vorhandene Bände

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