期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
型为gᵘ 的 RHDTS的存在性
- (河北师范大学 数学科学学院,河北 石家庄 050024)
-
DOI：10.13763/j.cnki.jhebnu.nse.202101018
The Existence of RHDTS of Type gᵘ
摘要/Abstract
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, hᵗ)的3-HDF存在的充要条件为n≥3, t≥4, 且nh(t-1)≡0(mod3). 以3-HDF为基础, 给出了型为gᵘ的RHDTS存在的充要条件为u≥3, gu≡0(mod3)且(g, u)≠(1, 6).
Abstract：
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, hᵗ) exists if and only if n≥3, t≥4, and nh（t-1）≡0（mod3）. Furthermore, we show that an RHDTS of type gᵘ exists if and only if u≥3, gu≡0（mod3）and(g, u)≠(1, 6).
关键词
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
参考文献 10
- [1] HANANI H. Balanced Incomplete Block Designs and Related Designs [J] . Discrete Math, 1975, 11:255-369. doi:10. 1016/0012-365X(75)90040-0
- [2] REES R, STINSON D R. On Resolvable Group Divisible Designs with Block Size 3 [J] . Ars Combin. , 1987, 23:107-120.
- [3] ASSAF A, HARTMAN A. Resolvable Group Divisible Designs with Block Size 3 [J] . Discrete Math, 1989, 77:5-20. doi:10. 1016/0012-365X(89)90346-4
- [4] REES R. Two New Direct Product-type Constructions for Resolvable Group Divisible Designs [J] . J Combin Des, 1993, 1(1):15-26. doi:10. 1002/jcd. 3180010104
- [5] SARVATE D G. All Directed GDDs with Block Size Three, λ1=0, Exist [J] . Util Math, 1984, 26:311-317.
- [6] SARVATE D G. Some Results on Directed and Cyclic Designs [J] . Ars Combin, 1985, 19(5):179-190.
- [7] GE G, LING A C H. Group Divisible Designs with Block Size Four and Group Type gum1 for Small g [J] . Discrete Math, 2004, 285:97-120. doi:10. 1016/j. disc. 2994. 04. 003
- [8] COLBOURN C J, DINITZ J H. CRC Handbook of Combinatorial Designs [M] . 2nd ed. Boca Raton FL:Chapman and Hall/CRC, 2007.
- [9] 李艳平. 区组长为3的有向带洞标架设计 [D] . 石家庄:河北师范大学, 2015. LI Yanping. Oriented Holey Frarnes with Block Size Three [D] . Shijiazhuang:Hebei Normal University, 2015.
- [10] BERMOND J C, GERMA A, SOTTEAU D. Resolvable Decomposition of K*n [J] . J Combin Theory Ser A, 1979, 26:179-185. doi:10. 1016/10097-3165(79)90067-0