Extremal Point Sets and Gorenstein Ideals

Anthony V. Geramita; Tadahito Harima; Yong Su Shin

doi:10.1006/aima.1998.1889

Extremal Point Sets and Gorenstein Ideals

Advances in Mathematics ◽

10.1006/aima.1998.1889 ◽

2000 ◽

Vol 152 (1) ◽

pp. 78-119 ◽

Cited By ~ 28

Author(s):

Anthony V. Geramita ◽

Tadahito Harima ◽

Yong Su Shin

Keyword(s):

Extremal Point ◽

Point Sets

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A fast algorithm for computing optimal rectilinear Steiner trees for extremal point sets

Algorithms and Computations - Lecture Notes in Computer Science ◽

10.1007/bfb0015438 ◽

1995 ◽

pp. 322-331 ◽

Cited By ~ 3

Author(s):

Siu-Wing Cheng ◽

Chi-Keung Tang

Keyword(s):

Fast Algorithm ◽

Extremal Point ◽

Steiner Trees ◽

Point Sets

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Optimal rectilinear steiner tree for extremal point sets

Algorithms and Computation - Lecture Notes in Computer Science ◽

10.1007/3-540-57568-5_284 ◽

1993 ◽

pp. 523-532 ◽

Cited By ~ 3

Author(s):

Siu-Wing Cheng ◽

Andrew Lim ◽

Ching-Ting Wu

Keyword(s):

Steiner Tree ◽

Extremal Point ◽

Point Sets ◽

Rectilinear Steiner Tree

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Standard monomials and extremal point sets

Discrete Mathematics ◽

10.1016/j.disc.2019.111785 ◽

2020 ◽

Vol 343 (4) ◽

pp. 111785

Author(s):

Tamás Mészáros

Keyword(s):

Extremal Point ◽

Point Sets ◽

Standard Monomials

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An O(k²n)-time algorithm for constructing an optimal rectilinear steiner tree for extremal point sets

10.14711/thesis-b447448 ◽

1994 ◽

Author(s):

Chi-keung Tang

Keyword(s):

Steiner Tree ◽

Time Algorithm ◽

Extremal Point ◽

Point Sets ◽

Rectilinear Steiner Tree

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A linear-time algorithm to construct a rectilinear Steiner minimal tree fork-extremal point sets

Algorithmica ◽

10.1007/bf01758761 ◽

1992 ◽

Vol 7 (1-6) ◽

pp. 247-276 ◽

Cited By ~ 16

Author(s):

D. S. Richards ◽

J. S. Salowe

Keyword(s):

Linear Time ◽

Time Algorithm ◽

Extremal Point ◽

Linear Time Algorithm ◽

Point Sets ◽

Minimal Tree ◽

Steiner Minimal Tree ◽

Tree Fork

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Representation of certain self-similar quasiperiodic tilings with perfect matching rules by discrete point sets

Journal de Physique I ◽

10.1051/jp1:1994234 ◽

1994 ◽

Vol 4 (6) ◽

pp. 893-904 ◽

Cited By ~ 4

Author(s):

Richard Klitzing ◽

Michael Baake

Keyword(s):

Perfect Matching ◽

Discrete Point ◽

Point Sets ◽

Self Similar ◽

Matching Rules ◽

Quasiperiodic Tilings

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Almost empty polygons

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.40.2003.3.1 ◽

2003 ◽

Vol 40 (3) ◽

pp. 269-286 ◽

Cited By ~ 4

Author(s):

H. Nyklová

Keyword(s):

Exact Results ◽

Point Sets ◽

Planar Point ◽

Convex Position ◽

Vertex Set ◽

Point Set ◽

Empty Polygons

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

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