The existence of strong complete mappings of finite groups: A survey

被引：11
|
作者：
Evans, Anthony B. [1 ]
机构：
[1] Wright State Univ, Dayton, OH 45435 USA
来源：
DISCRETE MATHEMATICS | 2013年 / 313卷 / 11期
关键词：
Complete mapping; Orthomorphism; Strong complete mapping; KNUT-VIK DESIGNS; ADMISSIBILITY; NONEXISTENCE;
D O I：
10.1016/j.disc.2011.11.040
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A complete mapping of a group G is a bijection theta: G -> G for which the mapping x x theta (x) is a bijection, and a strong complete mapping of a group G is a complete mapping theta of G for which the mapping x x(-1)theta(x) is also a bijection. Complete mappings and strong complete mappings have several combinatorial applications. While the existence problem for complete mappings of finite groups has been settled, very little is known about the existence of strong complete mappings of finite groups. We survey the known existence results for strong complete mappings of finite groups and we suggest directions for further work on this existence problem. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码：1191 / 1196
页数：6
相关论文
共 50 条
  • [1] The Existence Problem for Strong Complete Mappings of Finite Groups
    Evans, Anthony B.
    COMBINATORICS, GRAPH THEORY AND COMPUTING, SEICCGTC 2021, 2024, 448 : 11 - 22
  • [2] The existence of strong complete mappings
    Evans, Anthony B.
    ELECTRONIC JOURNAL OF COMBINATORICS, 2012, 19 (01):
  • [3] COMPLETE MAPPINGS OF FINITE GROUPS
    PAIGE, LJ
    BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1951, 57 (01) : 77 - 78
  • [4] Strong complete mappings for 3-groups
    Akhtar, Reza
    Gagola, Stephen M., III
    DISCRETE MATHEMATICS, 2022, 345 (01)
  • [5] PARTITIONS OF GROUPS AND COMPLETE MAPPINGS
    FRIEDLANDER, RJ
    GORDON, B
    TANNENBAUM, P
    PACIFIC JOURNAL OF MATHEMATICS, 1981, 92 (02) : 283 - 293
  • [6] COMPLETE MAPPINGS OF FINITE-FIELDS
    NIEDERREITER, H
    ROBINSON, KH
    JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1982, 33 (OCT): : 197 - 212
  • [7] Existence of Fixed Points for Expansive Mappings in Complete Strong Altering JS']JS-metric space
    Varunnya, X. M. Jeffin
    Gnanachandra, P.
    Anandapriya, B.
    BAGHDAD SCIENCE JOURNAL, 2023, 20 (01) : 326 - 331
  • [8] ON FINITE COMPLETE GROUPS
    HARTLEY, B
    ROBINSON, DJS
    ARCHIV DER MATHEMATIK, 1980, 35 (1-2) : 67 - 74
  • [9] Existence of fixed points for mappings of finite sets
    V. I. Danilov
    G. A. Koshevoi
    Mathematical Notes, 2007, 82 : 174 - 179
  • [10] Existence of fixed points for mappings of finite sets
    Danilov, V. I.
    Koshevoi, G. A.
    MATHEMATICAL NOTES, 2007, 82 (1-2) : 174 - 179
12345