On order and metric convexities in Z n

M. Changat; A. Vijayakumar

Compositio Mathematica (1992)

  • Volume: 82, Issue: 1, page 57-65
  • ISSN: 0010-437X

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Changat, M., and Vijayakumar, A.. "On order and metric convexities in $Z^n$." Compositio Mathematica 82.1 (1992): 57-65. <http://eudml.org/doc/90147>.

@article{Changat1992,
author = {Changat, M., Vijayakumar, A.},
journal = {Compositio Mathematica},
keywords = {integer lattice; Carathéodory; Helly; Radon; Tverberg},
language = {eng},
number = {1},
pages = {57-65},
publisher = {Kluwer Academic Publishers},
title = {On order and metric convexities in $Z^n$},
url = {http://eudml.org/doc/90147},
volume = {82},
year = {1992},
}

TY - JOUR
AU - Changat, M.
AU - Vijayakumar, A.
TI - On order and metric convexities in $Z^n$
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 82
IS - 1
SP - 57
EP - 65
LA - eng
KW - integer lattice; Carathéodory; Helly; Radon; Tverberg
UR - http://eudml.org/doc/90147
ER -

References

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  1. [1] L. Danzer, B. Grunbaum and V. Klee, Helly's theorem and its relatives, Amer. Math. Soc. Proc. of Symposia in Pure Mathematics7 (1963) 101-180. Zbl0132.17401MR157289
  2. [2] J.P. Doignon, Convexity in Crystallographical lattices, J. Geometry3 (1973), 71-85. Zbl0245.52004MR387090
  3. [3] S.P. Franklin, Some results on order convexity, Amer. Math. Monthly69 (1962) 357-359. Zbl0106.24401MR1531672
  4. [4] R.E. Jamison, Partition numbers for trees and ordered sets, Pacific J. Math., 96 (1981) 115-140. Zbl0482.52010MR634767
  5. [5] M. Lassak, The Helly dimension for Cartesian products of metric spaces, Mat. Issled, 10(2) (1975) 159-167. Zbl0338.54020MR397566
  6. [6] F.W. Levi, On Helly theorem and the axioms of convexity, J. Indian Math. Soc., 15 Part A (1951) 65-76. Zbl0044.19101MR43487
  7. [7] E. Sampathkumar, Convex sets in a graph, Ind. J. Pure. Appl. Maths., 15(10) (1984), 1065-1071. Zbl0563.52001MR765010
  8. [8] G. Sierksma, Caratheodory and Helly numbers of convex product structures, Pacific J. Math.61 (1975), 275-282. Zbl0301.52002MR397562
  9. [9] V.P. Soltan, Some questions in the abstract theory of convexity, Soviet Math. Dokl., 17(3) (1976), 730-733. Zbl0348.52002
  10. [10] V.P. Soltan, d-convexity in finite metric spaces, Bull. Akad. Stince RSS, Moldoven No. 2, 94 (1978), 29-33. Zbl0394.52001MR509511
  11. [11] A. Vijayakumar, Some characterization theorems for the discrete holometric space, Collect. Math.38 (1987), 123-129. Zbl0668.51011MR988950

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