Discrete torsion and its application for a generalized van der Waerden's theorem

被引：4

作者：

Blair, David E. ^{[1
]}

Konno, Tatsuo ^{[2
]}

机构：

[1] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

[2] Nihon Univ, Coll Engn, Koriyama, Fukushima 9638642, Japan

来源：

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | 2011年 / 87卷 / 10期

关键词：

Discrete curvature; discrete torsion; polygonal line;

D O I：

10.3792/pjaa.87.209

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we study discrete curvature and torsion for spatial polygonal lines of unit sides. We express geometric conditions on polygons by using inner products of oriented sides. As a application, we prove a generalization of van der Waerden's theorem. The theorem given in this paper and its proof clarify how the conditions on the sides affect the polygon being planar from the discrete torsion point of view.

引用

页码：209 / 214

页数：6

共 50 条

[1] ON THE INFINITARY VAN DER WAERDEN'S THEOREM
Mohsenipour, Shahram
[J]. TRANSACTIONS ON COMBINATORICS, 2024, 13 (04) : 319 - 325
[2] Random Van der Waerden Theorem
Zohar, Ohad
[J]. ELECTRONIC JOURNAL OF COMBINATORICS, 2022, 29 (01):
[3] On a generalization of the van der Waerden Theorem
Hirschfeld, Rudi
[J]. EUROPEAN JOURNAL OF COMBINATORICS, 2009, 30 (02) : 617 - 621
[4] A constructive topological proof of van der Waerden's theorem
Coquand, T
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 1995, 105 (03) : 251 - 259
[5] Superfilters, Ramsey theory, and van der Waerden's Theorem
Samet, Nadav
Tsaban, Boaz
[J]. TOPOLOGY AND ITS APPLICATIONS, 2009, 156 (16) : 2659 - 2669
[6] A VARIANT OF THE PROOF OF VAN DER WAERDEN'S THEOREM BY FURSTENBERG
Eyidogan, Sadik
Ozkurt, Ali Arslan
[J]. COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, 2021, 70 (02): : 1065 - 1072
[7] An infinitary polynomial van der Waerden theorem
McCutcheon, R
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 1999, 86 (02) : 214 - 231
[8] On generalized van der Waerden triples
Landman, B
Robertson, A
[J]. DISCRETE MATHEMATICS, 2002, 256 (1-2) : 279 - 290
[9] Proof of van der Waerden’s Theorem in Nine Figures
Blondal A.
Jungić V.
[J]. Arnold Mathematical Journal, 2018, 4 (2) : 161 - 168
[10] An analogue of a theorem of van der Waerden, and its application to two-distance preserving mappings
Alexandrov, Victor
[J]. PERIODICA MATHEMATICA HUNGARICA, 2016, 72 (02) : 252 - 257

← 1 2 3 4 5 →