Orientation-preserving and orientation-reversing mappings: a new description

被引：8
|
作者：
Higgins, Peter M. [1 ]
Vernitski, Alexei [1 ]
机构：
[1] Univ Essex, Dept Math Sci, Colchester CO4 3SQ, Essex, England
来源：
SEMIGROUP FORUM | 2022年 / 104卷 / 02期
关键词：
Orientation-preserving; Transformation semigroup;
D O I：
10.1007/s00233-022-10256-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We characterise the respective semigroups of mappings that preserve, or that preserve or reverse orientation of a finite cycle, in terms of their actions on oriented triples and oriented quadruples. This leads to a proof that the latter semigroup coincides with the semigroup of all mappings that preserve intersections of chords on the corresponding circle.
引用
收藏
页码：509 / 514
页数：6
相关论文
共 50 条
  • [41] On the geometry of orientation-preserving planar piecewise isometries
    Ashwin, P
    Fu, XC
    JOURNAL OF NONLINEAR SCIENCE, 2002, 12 (03) : 207 - 240
  • [42] On the Geometry of Orientation-Preserving Planar Piecewise Isometries
    Journal of Nonlinear Science, 2002, 12 : 207 - 240
  • [43] The semigroups of orientation-preserving transformations with restricted range
    Zhao, Ping
    Hu, Huabi
    FILOMAT, 2024, 38 (12) : 4241 - 4251
  • [44] On classification of cyclic orientation-reversing actions of big order on closed surfaces
    Gromadzki, G.
    Szepietowski, B.
    Zhao, X.
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2016, 220 (01) : 465 - 481
  • [45] The monoid of orientation-preserving k-extensive transformations
    De Biao Li
    Wen Ting Zhang
    Yan Feng Luo
    Semigroup Forum, 2022, 104 : 376 - 397
  • [46] Rotation numbers of discontinuous orientation-preserving circle maps
    Brette, R
    SET-VALUED ANALYSIS, 2003, 11 (04): : 359 - 371
  • [47] Rotation Numbers of Discontinuous Orientation-Preserving Circle Maps
    Romain Brette
    Set-Valued Analysis, 2003, 11 : 359 - 371
  • [48] The monoid of orientation-preserving k-extensive transformations
    Li, De Biao
    Zhang, Wen Ting
    Luo, Yan Feng
    SEMIGROUP FORUM, 2022, 104 (02) : 376 - 397
  • [49] Continuous and Orientation-preserving Correspondences via Functional Maps
    Ren, Jing
    Poulenard, Adrien
    Wonka, Peter
    Ovsjanikov, Maks
    ACM TRANSACTIONS ON GRAPHICS, 2018, 37 (06):
  • [50] Continuous and Orientation-preserving Correspondences via Functional Maps
    Ren, Jing
    Poulenard, Adrien
    Wonka, Peter
    Ovsjanikov, Maks
    SIGGRAPH ASIA'18: SIGGRAPH ASIA 2018 TECHNICAL PAPERS, 2018,
12345