Rank relations between a {0, 1}-matrix and its complement

Ma, Chao; Zhong, Jin

doi:10.1515/math-2018-0020

Cited by 1 publication

(2 citation statements)

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“…is the complement of a (0, 1)-matrix A t × u [see Ma and Zhong [31] , I J I n c n n , A T is the transpose of a matrix A, α = circ (0 1 0…0) is the basic circulant matrix of order n such that α n = I n and A × B denotes Kronecker product of two matrices A and B (see Hall [18] ). EA g p C C C n p p p ( ) | u u u  (n copies) denotes the elementary abelian group of order g and C p = EA(p) is a cyclic group of order p where p is a prime.…”

Section: Introductionmentioning

confidence: 99%

“…Notations: I n denotes the identity matrix of order n, J t × u is the t × u matrix all of whose entries are 1, in particular Jn=Jn×n. At×uc=Jt×u−At×u is the complement of a (0, 1)-matrix A t × u [see Ma and Zhong [31] , Inc=Jn−In, AT is the transpose of a matrix A , α = circ (0 1 0…0) is the basic circulant matrix of order n such that α n = I n and A × B denotes Kronecker product of two matrices A and B (see Hall [18] ). g=pn ( n copies) denotes the elementary abelian group of order g and C p = EA(p) is a cyclic group of order p where p is a prime.…”

Section: Introductionmentioning

confidence: 99%

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On Certain Classes of Rectangular Designs

Singh

Saurabh

2023

Calcutta Statistical Association Bulletin

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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

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Section: Introductionmentioning

confidence: 99%