型为g^(u)的RHDTS的存在性  

The Existence of RHDTS of Type g^(u)

作　　者：璩雪娇 郭志芬 田子红[1] QU Xuejiao;GUO Zhifen;TIAN Zihong(School of Mathematical Sciences,Hebei Normal University,Hebei Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,河北石家庄050024

出　　处：《河北师范大学学报（自然科学版）》2021年第6期553-558,共6页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(11871019)。

摘　　要：有向可分组设计是指区组形式为可迁三元组的可分组设计,如果所有区组可以划分成若干个平行类,则称其为可分解的有向可分组设计.首先讨论了带洞有向标架设计,证明了型为(n,h^(t))的3-HDF存在的充要条件为n≥3,t≥4,且nh(t-1)≡0(mod 3).以3-HDF为基础,给出了型为g^(u)的RHDTS存在的充要条件为u≥3,g^(u)≡0(mod 3)且(g,u)≠(1,6).A directed group divisible design is a group divisible design whose blocks are directed triples.If all of the blocks can be partitioned into parallel classes,then It is called an resolvable.In this paper,we first investigate holey directed frame.We prove that a 3-HDF of type(n,h^(t))exists if and only if n≥3,t≥4,and nh(t-1)≡0(mod 3).Furthermore,we show that an RHDTS of type g^(u) exists if and only if u≥3,gu≡0(mod 3)and(g,u)≠(1,6).

关 键 词：可分组设计 可分解的有向可分组设计 带洞有向标架 

分 类 号：O157.2[理学—数学]