A NOTE ON BOUNDS ON THE MINIMUM AREA OF CONVEX LATTICE POLYGONS

被引：4

作者：

COLBOURN, CJ ^{[1
]}

SIMPSON, RJ ^{[1
]}

机构：

[1] CURTIN UNIV TECHNOL,SCH MATH & STAT,PERTH,WA 6001,AUSTRALIA

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 1992年 / 45卷 / 02期

关键词：

D O I：

10.1017/S0004972700030094

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The minimum area a(v) of a v-sided convex lattice polygon is known to satisfy (v/2) less-than-or-equal-to a(2v) less-than-or-equal-to (v/3) -v+1. We conjecture that a(v) = cv3 + o(v3), for c a constant; we prove that a(v) less-than-or-equal-to (15/784)v3 + o(v3), and that for some positive constant c, a(v) greater-than-or-equal-to cv2.5.

引用

页码：237 / 240

页数：4

共 50 条

[41] Size and area of square lattice polygons
Jensen, I
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2000, 33 (18): : 3533 - 3543
[42] Tight Bounds on the Maximal Area of Small Polygons: Improved Mossinghoff Polygons
Bingane, Christian
DISCRETE & COMPUTATIONAL GEOMETRY, 2023, 70 (01) : 236 - 248
[43] A CENSUS OF CONVEX LATTICE POLYGONS WITH AT MOST ONE INTERIOR LATTICE POINT
RABINOWITZ, S
ARS COMBINATORIA, 1989, 28 : 83 - 96
[44] THE LIMIT SHAPE OF CONVEX LATTICE POLYGONS AND RELATED TOPICS
VERSHIK, AM
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1994, 28 (01) : 13 - 20
[45] AN ANALOGUE OF THE ALEKSANDROV PROJECTION THEOREM FOR CONVEX LATTICE POLYGONS
Zhang, Ning
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145 (06) : 2305 - 2310
[46] NUMBER OF ALMOST-CONVEX POLYGONS ON THE SQUARE LATTICE
LIN, KY
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1992, 25 (07): : 1835 - 1842
[47] Limit shape of convex lattice polygons with minimal perimeter
Prodromou, MN
DISCRETE MATHEMATICS, 2005, 300 (1-3) : 139 - 151
[48] ENUMERATION OF ALMOST-CONVEX POLYGONS ON THE SQUARE LATTICE
ENTING, IG
GUTTMANN, AJ
RICHMOND, LB
WORMALD, NC
RANDOM STRUCTURES & ALGORITHMS, 1992, 3 (04) : 445 - 461
[49] Tight bounds on the maximal perimeter of convex equilateral small polygons
Christian Bingane
Charles Audet
Archiv der Mathematik, 2022, 119 : 325 - 336
[50] Tight bounds on the maximal perimeter of convex equilateral small polygons
Bingane, Christian
Audet, Charles
ARCHIV DER MATHEMATIK, 2022, 119 (03) : 325 - 336

← 1 2 3 4 5 →