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Volumn 39, Issue 4, 2002, Pages 533-555

From deep holes to free planes

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EID: 0036790310     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0273-0979-02-00950-3     Document Type: Article
Times cited : (22)

References (54)
  • 1
    • 0010739372 scopus 로고
    • On lattice coverings by spheres
    • MR 15:780c
    • R.P. Bambah, On lattice coverings by spheres, Proc. Nat. Inst. Sci. India 20 (1954), 25-52. MR 15:780c.
    • (1954) Proc. Nat. Inst. Sci. India , vol.20 , pp. 25-52
    • Bambah, R.P.1
  • 2
    • 0000303291 scopus 로고
    • New bounds in some transference theorems in the geometry of numbers
    • MR 94k:11075
    • W. Banaszczyk, New bounds in some transference theorems in the geometry of numbers, Math. Ann. 296 (1993), 625-636. MR 94k:11075.
    • (1993) Math. Ann. , vol.296 , pp. 625-636
    • Banaszczyk, W.1
  • 3
    • 0002184625 scopus 로고
    • Closest packing and loosest covering of the space with balls
    • MR 88g:52003
    • K. Böröczky, Closest packing and loosest covering of the space with balls, Studia Sci. Math. Hungar. 21 (1986), 79-89. MR 88g:52003.
    • (1986) Studia Sci. Math. Hungar. , vol.21 , pp. 79-89
    • Böröczky, K.1
  • 4
    • 0001841408 scopus 로고    scopus 로고
    • Translational and homothetic clouds for a convex body
    • MR 97h:52008
    • K. Böröczky and V. Soltan, Translational and homothetic clouds for a convex body, Studia Sci. Math. Hungar. 32 (1996), 93-102. MR 97h:52008.
    • (1996) Studia Sci. Math. Hungar. , vol.32 , pp. 93-102
    • Böröczky, K.1    Soltan, V.2
  • 5
    • 84855625833 scopus 로고    scopus 로고
    • The longest segment in the complement of a packing
    • in press
    • K. Böröczky Jr. and G. Tardos, The longest segment in the complement of a packing, Mathematika, in press.
    • Mathematika
    • Böröczky K., Jr.1    Tardos, G.2
  • 6
    • 0000848517 scopus 로고
    • Simultaneous packing and covering in Euclidean space
    • MR 47:7600
    • G.J. Butler, Simultaneous packing and covering in Euclidean space, Proc. London Math. Soc. 25 (1972), 721-735. MR 47:7600.
    • (1972) Proc. London Math. Soc. , vol.25 , pp. 721-735
    • Butler, G.J.1
  • 9
    • 84976043625 scopus 로고
    • Covering space with equal spheres
    • MR 23:A2131
    • H.S.M. Coxeter, L. Few and C.A. Rogers, Covering space with equal spheres, Mathematika 6 (1959), 147-157. MR 23:A2131.
    • (1959) Mathematika , vol.6 , pp. 147-157
    • Coxeter, H.S.M.1    Few, L.2    Rogers, C.A.3
  • 10
    • 0000904907 scopus 로고
    • The number of congruent spheres that hide a given sphere of three-dimensional space is not less than 30
    • MR 82m:52008
    • G. Csóka, The number of congruent spheres that hide a given sphere of three-dimensional space is not less than 30, Studia Sci. Math. Hungar. 12 (1977), 323-334. MR 82m:52008.
    • (1977) Studia Sci. Math. Hungar. , vol.12 , pp. 323-334
    • Csóka, G.1
  • 11
    • 0001376566 scopus 로고
    • Drei beispieie zu lagerungsproblemen
    • L. Danzer, Drei Beispieie zu Lagerungsproblemen, Arch. Math. 11 (1960), 159-165.
    • (1960) Arch. Math. , vol.11 , pp. 159-165
    • Danzer, L.1
  • 12
    • 0010741349 scopus 로고
    • Solution of the problem of least dense lattice covering of a four-dimensional space by equal spheres
    • B.N. Delone and S.S. Ryskov, Solution of the problem of least dense lattice covering of a four-dimensional space by equal spheres, Soviet Math. Dokl. 4 (1963), 1333-1334; Dokl. Acad. Nauk SSSR 152 (1963), 523-524. MR 31:126.
    • (1963) Soviet Math. Dokl. , vol.4 , pp. 1333-1334
    • Delone, B.N.1    Ryskov, S.S.2
  • 13
    • 0010703480 scopus 로고
    • MR 31:126
    • B.N. Delone and S.S. Ryskov, Solution of the problem of least dense lattice covering of a four-dimensional space by equal spheres, Soviet Math. Dokl. 4 (1963), 1333-1334; Dokl. Acad. Nauk SSSR 152 (1963), 523-524. MR 31:126.
    • (1963) Dokl. Acad. Nauk SSSR , vol.152 , pp. 523-524
  • 14
    • 0002337176 scopus 로고
    • Packing and covering with convex sets
    • eds. P.M. Gruber and J.M. Wills, North-Holland, Amsterdam. MR 95d:52020
    • G. Fejes Tóth and W. Kuperberg, Packing and Covering with Convex Sets, Handbook of Convex Geometry (eds. P.M. Gruber and J.M. Wills), North-Holland, Amsterdam (1993), 799-860. MR 95d:52020.
    • (1993) Handbook of Convex Geometry , pp. 799-860
    • Fejes Tóth, G.1    Kuperberg, W.2
  • 15
    • 0000135054 scopus 로고
    • Verdeckung einer kugel durch kugeln
    • MR 22:4017
    • L. Fejes Tóth, Verdeckung einer Kugel durch Kugeln, Publ. Math. Debrecen 6 (1959), 234-240. MR 22:4017.
    • (1959) Publ. Math. Debrecen , vol.6 , pp. 234-240
    • Fejes Tóth, L.1
  • 16
    • 0010703319 scopus 로고
    • Close packing and loose covering with balls
    • MR 55:1224
    • L. Fejes Tóth, Close packing and loose covering with balls, Publ. Math. Debrecen 23 (1976), 323-326. MR 55:1224.
    • (1976) Publ. Math. Debrecen , vol.23 , pp. 323-326
    • Fejes Tóth, L.1
  • 18
    • 0000499135 scopus 로고
    • Transillumination of lattice packing of balls
    • MR 94h:52032
    • T. Hausel, Transillumination of lattice packing of balls, Studia Sci. Math. Hungar. 27 (1992), 241-242. MR 94h:52032.
    • (1992) Studia Sci. Math. Hungar. , vol.27 , pp. 241-242
    • Hausel, T.1
  • 19
  • 21
    • 84983708098 scopus 로고    scopus 로고
    • Segments in ball packings
    • in press
    • M. Henk and C. Zong, Segments in ball packings, Mathematika, in press.
    • Mathematika
    • Henk, M.1    Zong, C.2
  • 23
    • 0002351144 scopus 로고
    • Ein satz über gitterförmige kugelpackungen
    • MR 24:A3562
    • A. Heppes, Ein Satz über gitterförmige Kugelpackungen: Ann. Univ. Sci. Budapest Sect. Math. 3-4 (1960/61), 89-90. MR 24:A3562.
    • (1960) Ann. Univ. Sci. Budapest Sect. Math. , vol.3-4 , pp. 89-90
    • Heppes, A.1
  • 24
    • 0001670394 scopus 로고
    • On the number of spheres which can hide a given sphere
    • MR 35:875
    • A. Heppes, On the number of spheres which can hide a given sphere, Canad. J. Math. 19 (1967), 413-418. MR 35:875.
    • (1967) Canad. J. Math. , vol.19 , pp. 413-418
    • Heppes, A.1
  • 25
    • 0002896983 scopus 로고
    • Durchleuchtung gitterformiger kugelpackungen mit lichtbündeln
    • MR 50:1131
    • I. Hortobágyi, Durchleuchtung gitterformiger Kugelpackungen mit Lichtbündeln, Studia Sci. Math. Hungar. 6 (1971), 147-150. MR 50:1131.
    • (1971) Studia Sci. Math. Hungar. , vol.6 , pp. 147-150
    • Hortobágyi, I.1
  • 26
    • 0001452226 scopus 로고
    • Über die durchsichtigkeit gitterförmiger kugelpackungen
    • MR 45:7615
    • J. Horváth, Über die Durchsichtigkeit gitterförmiger Kugelpackungen, Studia Sci. Math. Hungar. 5 (1970), 421-426. MR 45:7615.
    • (1970) Studia Sci. Math. Hungar. , vol.5 , pp. 421-426
    • Horváth, J.1
  • 29
    • 0010658150 scopus 로고    scopus 로고
    • Eine bemerkung zur durchleuchtung von gitterförmigen kugelpackungen
    • Thessalohiki. MR 98h:52034
    • J. Horváth, Eine Bemerkung zur Durchleuchtung von gitterförmigen Kugelpackungen, Proc. Internat. Conf. Geom., Thessalohiki, 1996, 187-191. MR 98h:52034.
    • (1996) Proc. Internat. Conf. Geom. , pp. 187-191
    • Horváth, J.1
  • 31
    • 0000927223 scopus 로고
    • Covering minima and lattice-point-free convex bodies
    • MR 89i:52020
    • R. Kannan and L. Lovász, Covering minima and lattice-point-free convex bodies, Ann. Math. 128 (1988), 577-602. MR 89i:52020.
    • (1988) Ann. Math. , vol.128 , pp. 577-602
    • Kannan, R.1    Lovász, L.2
  • 32
    • 0003262982 scopus 로고
    • Sur les formes quadratiques positives quaternaires
    • A.N. Korkin and E.I. Zolotarev, Sur les formes quadratiques positives quaternaires, Math. Ann. 5 (1872), 581-583.
    • (1872) Math. Ann. , vol.5 , pp. 581-583
    • Korkin, A.N.1    Zolotarev, E.I.2
  • 33
    • 0040156836 scopus 로고
    • Sur les formes quadratiques positives
    • A.N. Korkin and E.I. Zolotarev, Sur les formes quadratiques positives, Math. Ann. 11 (1877), 242-292.
    • (1877) Math. Ann. , vol.11 , pp. 242-292
    • Korkin, A.N.1    Zolotarev, E.I.2
  • 34
    • 0010702673 scopus 로고
    • On the minimum determinant and the circumscribed hexagons of a convex domain
    • MR 9:10h
    • K. Mahler, On the minimum determinant and the circumscribed hexagons of a convex domain, Proc. Kon. Ned. Akad. Wet. 50 (1947), 692-703. MR 9:10h.
    • (1947) Proc. Kon. Ned. Akad. Wet. , vol.50 , pp. 692-703
    • Mahler, K.1
  • 36
    • 84967713986 scopus 로고
    • A bound for the covering radius of the Leech lattice
    • MR 84m:10022a
    • S.P. Norton, A bound for the covering radius of the Leech lattice, Proc. Royal Soc. London A 380 (1982), 259-260. MR 84m:10022a.
    • (1982) Proc. Royal Soc. London A , vol.380 , pp. 259-260
    • Norton, S.P.1
  • 37
    • 84963044617 scopus 로고
    • On positive definite quadratic forms
    • MR 14:1065g
    • R.A. Rankin, On positive definite quadratic forms, J. London Math. Soc. 28 (1953), 309-314. MR 14:1065g.
    • (1953) J. London Math. Soc. , vol.28 , pp. 309-314
    • Rankin, R.A.1
  • 38
    • 0010738983 scopus 로고
    • Über die dichteste gitterförmige lagerung kongruenter bereiche in der ebene und eine besondere art konvexer kurven
    • K. Reinhardt, Über die dichteste gitterförmige Lagerung kongruenter Bereiche in der Ebene und eine besondere Art konvexer Kurven, Abh. Math. Sem. Hamburg 10 (1934), 216-230.
    • (1934) Abh. Math. Sem. Hamburg , vol.10 , pp. 216-230
    • Reinhardt, K.1
  • 39
    • 84963002094 scopus 로고
    • A note on coverings and packings
    • MR 13:323b
    • C.A. Rogers, A note on coverings and packings, J. London Math. Soc. 25 (1950), 327-331. MR 13:323b.
    • (1950) J. London Math. Soc. , vol.25 , pp. 327-331
    • Rogers, C.A.1
  • 40
    • 0000665771 scopus 로고
    • The packing of equal spheres
    • MR 21:847
    • C.A. Rogers, The packing of equal spheres, Proc. London Math. Soc. 8 (1958), 609-620. MR 21:847.
    • (1958) Proc. London Math. Soc. , vol.8 , pp. 609-620
    • Rogers, C.A.1
  • 41
    • 84976024989 scopus 로고
    • Lattice coverings of space
    • MR 23:A2130
    • C.A. Rogers, Lattice coverings of space, Mathematika 6 (1959), 33-39. MR 23:A2130.
    • (1959) Mathematika , vol.6 , pp. 33-39
    • Rogers, C.A.1
  • 42
    • 0004279601 scopus 로고
    • Cambridge University Press, Cambridge. MR 30:2405
    • C.A. Rogers, Packing and Covering, Cambridge University Press, Cambridge, 1964. MR 30:2405.
    • (1964) Packing and Covering
    • Rogers, C.A.1
  • 43
    • 0010703483 scopus 로고
    • Solution of the problem of least dense lattice covering of five-dimensional space by equal spheres
    • MR 55:273
    • S.S. Ryskov and E.P. Baranovskii, Solution of the problem of least dense lattice covering of five-dimensional space by equal spheres, Soviet Math. Dokl. 16 (1975), 586-590. MR 55:273.
    • (1975) Soviet Math. Dokl. , vol.16 , pp. 586-590
    • Ryskov, S.S.1    Baranovskii, E.P.2
  • 44
    • 0010662218 scopus 로고
    • Estimation of the radius of a cylinder that can be embedded in every lattice packing of n-dimensional unit balls
    • MR 51:6600
    • S.S. Ryskov and J. Horváth, Estimation of the radius of a cylinder that can be embedded in every lattice packing of n-dimensional unit balls, Math. Notes 17 (1975), 72-75. MR 51:6600.
    • (1975) Math. Notes , vol.17 , pp. 72-75
    • Ryskov, S.S.1    Horváth, J.2
  • 45
    • 0001680397 scopus 로고
    • A mean value theorem in the geometry of numbers
    • MR 6:257b
    • C.L. Siegel, A mean value theorem in the geometry of numbers, Ann. Math. (2) 46 (1945), 340-347. MR 6:257b.
    • (1945) Ann. Math. , vol.46 , Issue.2 , pp. 340-347
    • Siegel, C.L.1
  • 46
    • 0010659277 scopus 로고    scopus 로고
    • On translational clouds for a convex body
    • MR 2001f:52041
    • I. Talata, On translational clouds for a convex body, Geom. Dedicata 80 (2000), 319-329. MR 2001f:52041.
    • (2000) Geom. Dedicata , vol.80 , pp. 319-329
    • Talata, I.1
  • 50
    • 0001514743 scopus 로고    scopus 로고
    • A problem of blocking light rays
    • MR 98g:52014
    • C. Zong, A problem of blocking light rays, Geom. Dedicata 67 (1997), 117-128. MR 98g:52014.
    • (1997) Geom. Dedicata , vol.67 , pp. 117-128
    • Zong, C.1
  • 51
    • 0033248815 scopus 로고    scopus 로고
    • A note on Hornich's problem
    • MR 99k:52026
    • C. Zong, A note on Hornich's problem, Arch. Math. 72 (1999), 127-131. MR 99k:52026.
    • (1999) Arch. Math. , vol.72 , pp. 127-131
    • Zong, C.1
  • 52
    • 0004025266 scopus 로고    scopus 로고
    • Springer-Verlag, New York. MR 2000g:52020
    • C. Zong, Sphere Packings, Springer-Verlag, New York, 1999. MR 2000g:52020.
    • (1999) Sphere Packings
    • Zong, C.1
  • 53
    • 0010745411 scopus 로고    scopus 로고
    • Simultaneous packing and covering in the Euclidean plane
    • CMP 2002:08
    • C. Zong, Simultaneous packing and covering in the Euclidean plane, Monatsh. Math. 134 (2002), 247-255. CMP 2002:08.
    • (2002) Monatsh. Math. , vol.134 , pp. 247-255
    • Zong, C.1
  • 54
    • 0038583826 scopus 로고    scopus 로고
    • Simultaneous packing and covering in three-dimensional Euclidean space
    • in press
    • C. Zong, Simultaneous packing and covering in three-dimensional Euclidean space, J. London Math. Soc., in press.
    • J. London Math. Soc.
    • Zong, C.1


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