On Certain Classes of Rectangular Designs

Author:

Singh Mithilesh Kumar1,Saurabh Shyam2ORCID

Affiliation:

1. Ranchi University, Ranchi, Jharkhand, India

2. Tata College, Kolhan University, Chaibasa, Jharkhand, India

Abstract

Rectangular designs are classified as regular, Latin regular, semi-regular, Latin semi-regular and singular designs. Some series of self-dual as well as α–resolvable designs which belong to the above classes are obtained. The building blocks of the designs are square (0, 1)-matrices. It is more general to view a class of designs based on an array than to view them based on disjoint groups of treatments of equal size. This generality enabled us to identify three subclasses of rectangular designs: Latin regular RDs, Latin semi-regular RDs and semi-regular L2-type designs which deserve further study. In every construction we obtain a matrix N with square (0, 1)-submatrices such that N becomes the incidence matrix of a rectangular design. The method is the reverse of the well-known tactical decomposition of the incidence matrix of a known design. The authors have already obtained some series of Group Divisible and L2-type designs using this method. Tactical decomposable designs are of great interest because of their connections with automorphisms of designs, see Bekar et al.[ 1 ] The rectangular designs constructed here are of statistical as well as combinatorial interest. AMS Subject Classification: 62K10, 05B05

Publisher

SAGE Publications

Subject

Statistics and Probability

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Certain Incomplete Block Designs from Combinatorial Matrices;Journal of the Indian Society for Probability and Statistics;2023-10-05

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