메뉴 건너뛰기




Volumn 53, Issue 1-2, 2006, Pages 59-69

The illumination conjecture and its extensions

Author keywords

Covering by homothets; Illumination by affine subspaces

Indexed keywords


EID: 33847294326     PISSN: 00315303     EISSN: 15882829     Source Type: Journal    
DOI: 10.1007/s10998-006-0021-4     Document Type: Article
Times cited : (24)

References (36)
  • 2
    • 0010603948 scopus 로고
    • The problem of illumination of the boundary of a convex body by affine subspaces
    • K. BEZDEK, The problem of illumination of the boundary of a convex body by affine subspaces, Mathematika 38 (1991), 362-375.
    • (1991) Mathematika , vol.38 , pp. 362-375
    • BEZDEK, K.1
  • 3
    • 0039442958 scopus 로고
    • Hadwiger's covering conjecture and its relatives
    • K. BEZDEK, Hadwiger's covering conjecture and its relatives, Amer. Math. Monthly 99 (1992), 954-956.
    • (1992) Amer. Math. Monthly , vol.99 , pp. 954-956
    • BEZDEK, K.1
  • 4
    • 0005329840 scopus 로고
    • On the illumination of smooth convex bodies
    • K. BEZDEK, On the illumination of smooth convex bodies, Arch. Math. 58 (1992), 611-614.
    • (1992) Arch. Math , vol.58 , pp. 611-614
    • BEZDEK, K.1
  • 5
    • 33846130490 scopus 로고    scopus 로고
    • K. BEZDEK, Research problem 46, Periodica Math. Hungar. 24 (1992), 119-121.
    • K. BEZDEK, Research problem 46, Periodica Math. Hungar. 24 (1992), 119-121.
  • 7
    • 33847314163 scopus 로고
    • A note on the illumination of convex bodies
    • K. BEZDEK, A note on the illumination of convex bodies, Geometriae Dedicate, 45 (1993), 89-91.
    • (1993) Geometriae Dedicate , vol.45 , pp. 89-91
    • BEZDEK, K.1
  • 8
    • 51649143595 scopus 로고    scopus 로고
    • K. BEZDEK, GY. KISS and M. MOLLARD, An illumination problem for zonoids, Israel J. Math. 81 (1993), 265-272.
    • K. BEZDEK, GY. KISS and M. MOLLARD, An illumination problem for zonoids, Israel J. Math. 81 (1993), 265-272.
  • 9
    • 0042147544 scopus 로고
    • On affine subspaces that illuminate a convex set
    • K. BEZDEK, On affine subspaces that illuminate a convex set, Beiträge zur Alg. und Geom. 35 (1994), 131-139.
    • (1994) Beiträge zur Alg. und Geom , vol.35 , pp. 131-139
    • BEZDEK, K.1
  • 10
    • 0010568089 scopus 로고    scopus 로고
    • A proof of Hadwiger's covering conjecture for dual cyclic polytopes
    • K. BEZDEK and T. BISZTRICZKY, A proof of Hadwiger's covering conjecture for dual cyclic polytopes, Geom. Dedicata 68 (1997), 29-41.
    • (1997) Geom. Dedicata , vol.68 , pp. 29-41
    • BEZDEK, K.1    BISZTRICZKY, T.2
  • 11
    • 33847300052 scopus 로고    scopus 로고
    • On the vertex index of convex bodies
    • accepted
    • K. BEZDEK and A. LITVAK, On the vertex index of convex bodies, Advances in Math., 1-20 (accepted).
    • Advances in Math , pp. 1-20
    • BEZDEK, K.1    LITVAK, A.2
  • 12
    • 33847312253 scopus 로고    scopus 로고
    • K. BEZDEK, ZS. LÁNGI, M. NASZÓDI and P. PAPEZ, Ball-polytopes, Preprint, Dept. of Math. and Stats., Univ. of Calgary, 2005, 1-24.
    • K. BEZDEK, ZS. LÁNGI, M. NASZÓDI and P. PAPEZ, Ball-polytopes, Preprint, Dept. of Math. and Stats., Univ. of Calgary, 2005, 1-24.
  • 13
    • 0007228724 scopus 로고
    • The problem of illuminating the boundary of a convex body
    • V. BOLTYANSKI, The problem of illuminating the boundary of a convex body, Izv. Mold. Fil. AN SSSR 76 (1960), 77-84.
    • (1960) Izv. Mold. Fil. AN SSSR , vol.76 , pp. 77-84
    • BOLTYANSKI, V.1
  • 14
    • 0010862327 scopus 로고    scopus 로고
    • A solution of the illumination problem for belt bodies
    • V. BOLTYANSKI, A solution of the illumination problem for belt bodies, Mat. Zametki 58 (1996), 505-511.
    • (1996) Mat. Zametki , vol.58 , pp. 505-511
    • BOLTYANSKI, V.1
  • 15
    • 33847323512 scopus 로고    scopus 로고
    • Solution of the illumination problem for three dimensional convex bodies
    • V. BOLTYANSKI, Solution of the illumination problem for three dimensional convex bodies, Dokl. Akad. Nauk 375 (2000), 298-301.
    • (2000) Dokl. Akad. Nauk , vol.375 , pp. 298-301
    • BOLTYANSKI, V.1
  • 16
    • 0035605484 scopus 로고    scopus 로고
    • Solution of the illumination problem for bodies with md M = 2
    • V. BOLTYANSKI, Solution of the illumination problem for bodies with md M = 2, Discrete Comput. Geom. 26 (2001), 527-541.
    • (2001) Discrete Comput. Geom , vol.26 , pp. 527-541
    • BOLTYANSKI, V.1
  • 17
    • 0040035064 scopus 로고    scopus 로고
    • Covering belt bodies by smaller homothetical copies
    • V. BOLTYANSKI and H. MARTINI, Covering belt bodies by smaller homothetical copies, Beiträge zur Alg. und Geom. 42 (2001), 313-324.
    • (2001) Beiträge zur Alg. und Geom , vol.42 , pp. 313-324
    • BOLTYANSKI, V.1    MARTINI, H.2
  • 19
    • 33847248965 scopus 로고    scopus 로고
    • 3 symmetric about a plane can be illuminated by 8 directions
    • 3 symmetric about a plane can be illuminated by 8 directions, J. Geom. 69/1-2 (2000), 37-50.
    • (2000) J. Geom , vol.69 , Issue.1-2 , pp. 37-50
    • DEKSTER, B.V.1
  • 20
    • 33847319240 scopus 로고
    • The star number of covering a space with convex bodies
    • P. ERDOS and C. A. ROGERS, The star number of covering a space with convex bodies, Acta Arith. 9 (1964), 41-45.
    • (1964) Acta Arith , vol.9 , pp. 41-45
    • ERDOS, P.1    ROGERS, C.A.2
  • 21
    • 0039655667 scopus 로고
    • A problem on covering of convex figures by similar figures
    • I. GOHBERG and A. MARKUS, A problem on covering of convex figures by similar figures, Izv. Mold. Fil. Akad. Nauk. SSSR 10 (1960), 87-90.
    • (1960) Izv. Mold. Fil. Akad. Nauk. SSSR , vol.10 , pp. 87-90
    • GOHBERG, I.1    MARKUS, A.2
  • 22
    • 33847317462 scopus 로고    scopus 로고
    • H. HADWIGER, Ungelöste Probleme, Nr. 38, Elem. Math. 15 (1960), 130-131.
    • H. HADWIGER, Ungelöste Probleme, Nr. 38, Elem. Math. 15 (1960), 130-131.
  • 23
    • 52849119783 scopus 로고    scopus 로고
    • Illumination problems and codes
    • GY. KISS, Illumination problems and codes, Periodica Math. Hungar. 39 (1999), 65-71.
    • (1999) Periodica Math. Hungar , vol.39 , pp. 65-71
    • GY1    KISS2
  • 25
    • 0039496320 scopus 로고
    • Covering the boundary of a convex set by tiles
    • M. LASSAK, Covering the boundary of a convex set by tiles, Proc. Amer. Math. Soc. 104 (1988), 269-272.
    • (1988) Proc. Amer. Math. Soc , vol.104 , pp. 269-272
    • LASSAK, M.1
  • 26
    • 0040206015 scopus 로고    scopus 로고
    • Illumination of three-dimensional convex bodies of constant width
    • Aristotle Univ. of Thessaloniki
    • M. LASSAK, Illumination of three-dimensional convex bodies of constant width, Proceedings of 4th Internat. Congress of Geometry, Aristotle Univ. of Thessaloniki, 1997, 246-250.
    • (1997) Proceedings of 4th Internat. Congress of Geometry , pp. 246-250
    • LASSAK, M.1
  • 27
    • 33847249460 scopus 로고    scopus 로고
    • H. MARTINI, Some results and problems around zonotopes, Coll. Math. Soc. J. Bolyai, Intuitive Geometry, Siófok 1985, North Holland 48 (1987), 383-418.
    • H. MARTINI, Some results and problems around zonotopes, Coll. Math. Soc. J. Bolyai, Intuitive Geometry, Siófok 1985, North Holland 48 (1987), 383-418.
  • 28
    • 0000679816 scopus 로고    scopus 로고
    • Combinatorial problems on the illumination of convex bodies
    • H. MARTINI and V. SOLTAN, Combinatorial problems on the illumination of convex bodies, Aeguationes Math. 57 (1999), 121-152.
    • (1999) Aeguationes Math , vol.57 , pp. 121-152
    • MARTINI, H.1    SOLTAN, V.2
  • 30
    • 0000227188 scopus 로고
    • The difference body of a convex body
    • C. A. ROGERS and G. C. SHEPHARD, The difference body of a convex body, Arch. Math. 8 (1957), 220-233.
    • (1957) Arch. Math , vol.8 , pp. 220-233
    • ROGERS, C.A.1    SHEPHARD, G.C.2
  • 31
    • 84971761881 scopus 로고
    • Illuminating sets of constant width
    • O. SCHRAMM, Illuminating sets of constant width, Mathematika 35 (1988), 180-189.
    • (1988) Mathematika , vol.35 , pp. 180-189
    • SCHRAMM, O.1
  • 32
    • 0040841951 scopus 로고
    • Illumination through convex bodies
    • P. SOLTAN and V. SOLTAN, Illumination through convex bodies, Dokl. Akad. Nauk. SSSR 286 (1986), 50-53.
    • (1986) Dokl. Akad. Nauk. SSSR , vol.286 , pp. 50-53
    • SOLTAN, P.1    SOLTAN, V.2
  • 33
    • 33847311355 scopus 로고    scopus 로고
    • arXiv:math.MG/0410144v1
    • K.J. SWANEPOEL, Quantitative illumination of convex bodies and vertex degrees of geometric Steiner minimal trees, arXiv:math.MG/0410144v1 (2004), 1-5.
    • (2004) , pp. 1-5
    • SWANEPOEL, K.J.1
  • 34
    • 0042228897 scopus 로고    scopus 로고
    • Solution of Hadwiger-Levi's covering problem for duals of cyclic 2k-polytopes
    • I. TALATA, Solution of Hadwiger-Levi's covering problem for duals of cyclic 2k-polytopes, Geom. Dedicata 74 (1999), 61-71.
    • (1999) Geom. Dedicata , vol.74 , pp. 61-71
    • TALATA, I.1
  • 35
    • 8744278412 scopus 로고    scopus 로고
    • Invariante Beleuchtung konvexer Körper
    • B. WEISSBACH, Invariante Beleuchtung konvexer Körper, Beiträge zur Alg. Geom. 37 (1996), 9-15.
    • (1996) Beiträge zur Alg. Geom , vol.37 , pp. 9-15
    • WEISSBACH, B.1
  • 36
    • 0013508028 scopus 로고
    • Some remarks concerning kissing numbers, blocking numbers and covering numbers
    • C. ZONG, Some remarks concerning kissing numbers, blocking numbers and covering numbers, Periodica Math. Hungar. 30 (1995), 233-238.
    • (1995) Periodica Math. Hungar , vol.30 , pp. 233-238
    • ZONG, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.