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(0, 1)-Matrices, Discrepancy and Preservers

Czechoslovak mathematical journal, 2019-12, Vol.69 (4), p.1123-1131 [Peer Reviewed Journal]

Mathematical Institute, Academy of Sciences of Cz 2019 ;Copyright Springer Nature B.V. 2019 ;ISSN: 0011-4642 ;EISSN: 1572-9141 ;DOI: 10.21136/CMJ.2019.0092-18

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Title:
(0, 1)-Matrices, Discrepancy and Preservers
Author: Beasley, LeRoy B.
Subjects: Analysis ; Boolean algebra ; Convex and Discrete Geometry ; Linear operators ; Mapping ; Mathematical analysis ; Mathematical Modeling and Industrial Mathematics ; Mathematics ; Mathematics and Statistics ; Matrix algebra ; Matrix methods ; Operators (mathematics) ; Ordinary Differential Equations
Is Part Of: Czechoslovak mathematical journal, 2019-12, Vol.69 (4), p.1123-1131
Description: Let m and n be positive integers, and let R = ( r 1 , . . . , r m ) and S = ( s 1 , . . . , s n ) be nonnegative integral vectors. Let A ( R , S ) be the set of all m × n (0, 1)-matrices with row sum vector R and column vector S . Let R and S be nonincreasing, and let F ( R ) be the m × n (0, 1)-matrix, where for each i , the i th row of F ( R , S ) consists of r i 1’s followed by ( n − r i ) 0’s. Let A ∈ A ( R , S ). The discrepancy of A, disc( A ), is the number of positions in which F ( R ) has a 1 and A has a 0. In this paper we investigate linear operators mapping m × n matrices over the binary Boolean semiring to itself that preserve sets related to the discrepancy. In particular, we show that bijective linear preservers of Ferrers matrices are either the identity mapping or, when m = n , the transpose mapping.
Publisher: Berlin/Heidelberg: Springer Berlin Heidelberg
Language: English
Identifier: ISSN: 0011-4642
EISSN: 1572-9141
DOI: 10.21136/CMJ.2019.0092-18
Source: Alma/SFX Local Collection

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(0, 1)-Matrices, Discrepancy and Preservers

Mathematical Institute, Academy of Sciences of Cz 2019 ;Copyright Springer Nature B.V. 2019 ;ISSN: 0011-4642 ;EISSN: 1572-9141 ;DOI: 10.21136/CMJ.2019.0092-18

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