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A note on magic rectangle set MRS Γ ( 2 k + 1 , 4 ; 4 l + 2 )
Author(s) -
Cichacz Sylwia,
Hinc Tomasz
Publication year - 2021
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21781
Subject(s) - rectangle , mathematics , combinatorics , abelian group , magic square , magic (telescope) , constant (computer programming) , set (abstract data type) , involution (esoterism) , order (exchange) , discrete mathematics , geometry , computer science , physics , finance , quantum mechanics , economics , programming language , politics , political science , law
A Γ ‐magic rectangle set M R S Γ ( a , b ; c ) of order a b c is a set of c arrays of size ( a × b ) whose entries are elements of a finite Abelian group Γ of order a b c , each appearing once, with all row sums in each rectangle equal to a constant ω ∈ Γ and all column sums in each rectangle equal to a constant δ ∈ Γ . There is known a complete characteristic of a MRS Γ ( a , b ; c ) for { a , b } ≠ { 2 k + 1 , 2 α } for positive integers k , α . The case { a , b } = { 2 k + 1 , 2 α } is unsolved for α > 1 . In this paper we show that a MRS Γ ( 2 k + 1 , 4 ; 4 l + 2 ) exists if and only if the group Γ has more than one involution.