当前位置: X-MOL 学术Discret. Math. › 论文详情
Globally simple Heffter arrays H(n;k) when k≡0,3(mod4)
Discrete Mathematics ( IF 0.728 ) Pub Date : 2020-01-13 , DOI: 10.1016/j.disc.2019.111787
Kevin Burrage; Diane M. Donovan; Nicholas J. Cavenagh; Emine Ş. Yazıcı

Square Heffter arrays are n×n arrays such that each row and each column contains k filled cells, each row and column sum is divisible by 2nk+1 and either x or −x appears in the array for each integer 1⩽x⩽nk. Archdeacon noted that a Heffter array, satisfying two additional conditions, yields a face 2-colourable embedding of the complete graph K2nk+1 on an orientable surface, where for each colour, the faces give a k-cycle system. Moreover, a cyclic permutation on the vertices acts as an automorphism of the embedding. These necessary conditions pertain to cyclic orderings of the entries in each row and each column of the Heffter array and are: (1) for each row and each column the sequential partial sums determined by the cyclic ordering must be distinct modulo 2nk+1; (2) the composition of the cyclic orderings of the rows and columns is equivalent to a single cycle permutation on the entries in the array. We construct Heffter arrays that satisfy condition (1) whenever (a) k≡0(mod4); or (b) n≡1(mod4) and k≡3(mod4); or (c) n≡0(mod4), k≡3(mod4) and n≫k. As corollaries to the above we obtain pairs of orthogonal k-cycle decompositions of K2nk+1.
更新日期:2020-01-21

 

全部期刊列表>>
2020新春特辑
限时免费阅读临床医学内容
ACS材料视界
科学报告最新纳米科学与技术研究
清华大学化学系段昊泓
自然科研论文编辑服务
中国科学院大学楚甲祥
上海纽约大学William Glover
中国科学院化学研究所
课题组网站
X-MOL
北京大学分子工程苏南研究院
华东师范大学分子机器及功能材料
中山大学化学工程与技术学院
试剂库存
天合科研
down
wechat
bug