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Volumn 34, Issue 3, 2005, Pages 391-409

Sums, projections, and sections of lattice sets, and the discrete covariogram

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EID: 23944469960     PISSN: 01795376     EISSN: 14320444     Source Type: Journal    
DOI: 10.1007/s00454-005-1169-z     Document Type: Article
Times cited : (39)

References (35)
  • 1
    • 0344088407 scopus 로고    scopus 로고
    • A fractional Helly theorem for convex lattice sets
    • I. Bárány and J. Matoušek, A fractional Helly theorem for convex lattice sets, Adv. Math. 174 (2003), 227-235.
    • (2003) Adv. Math. , vol.174 , pp. 227-235
    • Bárány, I.1    Matoušek, J.2
  • 2
    • 0039848599 scopus 로고    scopus 로고
    • Asymptotic formulae for the lattice point enumerator
    • U. Betke and K. Böröczky, Jr., Asymptotic formulae for the lattice point enumerator, Canad. J. Math. 51 (1999), 225-249.
    • (1999) Canad. J. Math. , vol.51 , pp. 225-249
    • Betke, U.1    Böröczky Jr., K.2
  • 3
    • 0036612671 scopus 로고    scopus 로고
    • Determining convex polygons from their covariograms
    • G. Bianchi, Determining convex polygons from their covariograms, Adv. in Appl Prob. 34 (2002), 261-266.
    • (2002) Adv. in Appl Prob. , vol.34 , pp. 261-266
    • Bianchi, G.1
  • 4
    • 23944469250 scopus 로고    scopus 로고
    • Matheron's conjecture for the covariogram problem
    • G. Bianchi, Matheron's conjecture for the covariogram problem, J. London Math. Soc. (2) 71 (2005), 203-220.
    • (2005) J. London Math. Soc. , vol.2 , Issue.71 , pp. 203-220
    • Bianchi, G.1
  • 6
    • 0037811210 scopus 로고    scopus 로고
    • An algorithm reconstructing lattice convex sets
    • S. Brunetti and A. Daurat, An algorithm reconstructing lattice convex sets, Theoret. Comput. Sci. 304 (2003), 35-57.
    • (2003) Theoret. Comput. Sci. , vol.304 , pp. 35-57
    • Brunetti, S.1    Daurat, A.2
  • 7
    • 0037357688 scopus 로고    scopus 로고
    • Estimation of mean particle volume using the set covariance function
    • A. Cabo and A. Baddeley, Estimation of mean particle volume using the set covariance function, Adv. in Appl. Probab. 35 (2003), 27-46.
    • (2003) Adv. in Appl. Probab. , vol.35 , pp. 27-46
    • Cabo, A.1    Baddeley, A.2
  • 8
    • 33947598548 scopus 로고
    • Cross-variance functions characterise bounded closed regular sets
    • Amsterdam
    • A. Cabo and R. H. P. Janssen, Cross-variance functions characterise bounded closed regular sets, CWI Technical Report, Amsterdam, 1994.
    • (1994) CWI Technical Report
    • Cabo, A.1    Janssen, R.H.P.2
  • 9
    • 8344225244 scopus 로고    scopus 로고
    • Discrete convexity and unimodularity - I
    • V. I. Danilov and G. A. Koshevoy, Discrete convexity and unimodularity - I, Adv. Math. 189 (2004), 301-324.
    • (2004) Adv. Math. , vol.189 , pp. 301-324
    • Danilov, V.I.1    Koshevoy, G.A.2
  • 10
    • 23944513497 scopus 로고    scopus 로고
    • 2
    • Presses Universitaires d'Orléans, Orléans
    • 2, in: CNR'IUT2000, vol. 1, Presses Universitaires d'Orléans, Orléans, 2000, pp. 341-350.
    • (2000) CNR'IUT2000 , vol.1 , pp. 341-350
    • Daurat, A.1
  • 13
    • 34250443845 scopus 로고
    • Convexity in crystollographical lattices
    • J.-P. Doignon, Convexity in crystollographical lattices, J. Geom. 3 (1973), 71-85.
    • (1973) J. Geom. , vol.3 , pp. 71-85
    • Doignon, J.-P.1
  • 14
    • 0004182159 scopus 로고
    • Cambridge University Press, New York, Corrections and update
    • R. J. Gardner, Geometric Tomography, Cambridge University Press, New York, 1995. Corrections and update available at http://www.ac.wwu.edu/~gardner.
    • (1995) Geometric Tomography
    • Gardner, R.J.1
  • 15
    • 21744459240 scopus 로고    scopus 로고
    • Discrete tomography: Determination of finite sets by X-rays
    • R. J. Gardner and P. Gritzmann, Discrete tomography: determination of finite sets by X-rays, Trans. Amer. Math. Soc. 349 (1997), 2271-2295.
    • (1997) Trans. Amer. Math. Soc. , vol.349 , pp. 2271-2295
    • Gardner, R.J.1    Gritzmann, P.2
  • 16
    • 0003043650 scopus 로고    scopus 로고
    • Uniqueness and complexity in discrete tomography
    • ed. by G. T. Herman and A. Kuba, Birkhäuser, Boston, MA
    • R. J. Gardner and P. Gritzmann, Uniqueness and complexity in discrete tomography, in: Discrete Tomography: Foundations, Algorithms and Application, ed. by G. T. Herman and A. Kuba, Birkhäuser, Boston, MA, 1999, pp. 85-113.
    • (1999) Discrete Tomography: Foundations, Algorithms and Application , pp. 85-113
    • Gardner, R.J.1    Gritzmann, P.2
  • 17
    • 23044529304 scopus 로고    scopus 로고
    • A Brunn-Minkowski inequality for the integer lattice
    • R. J. Gardner and P. Gronchi, A Brunn-Minkowski inequality for the integer lattice, Trans. Amer. Math. Soc. 353 (2001), 3995-4024.
    • (2001) Trans. Amer. Math. Soc. , vol.353 , pp. 3995-4024
    • Gardner, R.J.1    Gronchi, P.2
  • 18
    • 0005899134 scopus 로고    scopus 로고
    • Affine inequalities and radial mean bodies
    • R. J. Gardner and G. Zhang, Affine inequalities and radial mean bodies, Amer. J. Math. 120 (1998), 493-504.
    • (1998) Amer. J. Math. , vol.120 , pp. 493-504
    • Gardner, R.J.1    Zhang, G.2
  • 20
    • 0000838163 scopus 로고
    • Lattice points
    • ed. by P. M. Gruber and J. M. Wills, North-Holland, Amsterdam
    • P. Gritzmann and J. M. Wills, Lattice points, in: Handbook of Convexity, ed. by P. M. Gruber and J. M. Wills, North-Holland, Amsterdam, 1993, pp. 765-797.
    • (1993) Handbook of Convexity , pp. 765-797
    • Gritzmann, P.1    Wills, J.M.2
  • 22
    • 0039023174 scopus 로고
    • On the determination of probability distributions of more dimensions by their projections
    • A. Heppes, On the determination of probability distributions of more dimensions by their projections, Acta Math. Acad. Sci. Hung. 6 (1956), 403-410.
    • (1956) Acta Math. Acad. Sci. Hung. , vol.6 , pp. 403-410
    • Heppes, A.1
  • 24
    • 0009830587 scopus 로고
    • Line-intercept distributions do not characterize plane sets
    • C. L. Mallows and J. M. C. Clark, Line-intercept distributions do not characterize plane sets, J. Appl. Probab. 7 (1970), 240-244.
    • (1970) J. Appl. Probab. , vol.7 , pp. 240-244
    • Mallows, C.L.1    Clark, J.M.C.2
  • 26
    • 0039148586 scopus 로고
    • A volume inequality concerning sections of convex sets
    • M. Meyer, A volume inequality concerning sections of convex sets, Bull. London Math. Soc. 20 (1988), 151-155.
    • (1988) Bull. London Math. Soc. , vol.20 , pp. 151-155
    • Meyer, M.1
  • 27
    • 0000094884 scopus 로고
    • On projections of probability distributions
    • A. Rényi, On projections of probability distributions, Acta Math. Acad. Sci. Hung. 3 (1952), 131-142.
    • (1952) Acta Math. Acad. Sci. Hung. , vol.3 , pp. 131-142
    • Rényi, A.1
  • 28
    • 0022769010 scopus 로고
    • A strong chord property for 4-connected convex digital sets
    • C. Ronse, A strong chord property for 4-connected convex digital sets, Comput. Vision Graphics Image Process. 35 (1986), 259-269.
    • (1986) Comput. Vision Graphics Image Process , vol.35 , pp. 259-269
    • Ronse, C.1
  • 30
    • 0005784901 scopus 로고    scopus 로고
    • On two inverse problems in mathematical morphology
    • ed. by E. R. Dougherty, Marcel Dekker, New York
    • M. Schmitt, On two inverse problems in mathematical morphology, in: Mathematical Morphology in Image Processing, ed. by E. R. Dougherty, Marcel Dekker, New York, pp. 151-169.
    • Mathematical Morphology in Image Processing , pp. 151-169
    • Schmitt, M.1
  • 32
    • 23944516979 scopus 로고
    • How to minimize the largest shadow of a finite set
    • Wiley Interscience, New York
    • A. J. Schwenk, How to minimize the largest shadow of a finite set, in: Graphs and Applications, Boulder, CO, 1982, Wiley Interscience, New York, 1985, pp. 279-294.
    • (1985) Graphs and Applications, Boulder, CO , vol.1982 , pp. 279-294
    • Schwenk, A.J.1
  • 33
    • 0042388750 scopus 로고
    • How small can the mean shadow of a set be?
    • A. J. Schwenk and J. I. Munro, How small can the mean shadow of a set be?, Amer. Math. Monthly 90 (1983), 325-329.
    • (1983) Amer. Math. Monthly , vol.90 , pp. 325-329
    • Schwenk, A.J.1    Munro, J.I.2
  • 35
    • 0028388756 scopus 로고
    • A partial digest approach to restriction site mapping
    • S.S. Skiena and G. Sundaram, A partial digest approach to restriction site mapping, Bull. Math. Biol. 56 (1994), 275-294.
    • (1994) Bull. Math. Biol. , vol.56 , pp. 275-294
    • Skiena, S.S.1    Sundaram, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.