Diagonally cyclic equitable rectangles

Anthony B. Evans; David Fear; Rebecca J. Stones

doi:10.1007/s10623-014-9977-x

Diagonally cyclic equitable rectangles

Anthony B. Evans, David Fear, Rebecca J. Stones

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

An equitable (r,c;v)-rectangle is an r×c matrix L=(l_ij) with symbols from (Formula presented.) in which each symbol appears in every row either (Formula presented.) or (Formula presented.) times and in every column either (Formula presented.) or (Formula presented.) times. We call L diagonally cyclic if l(_i+1) (_j+1)=l_ij+1, where the rows are indexed by (Formula presented.) and columns indexed by (Formula presented.). We give a constructive proof of necessary and sufficient conditions for the existence of a diagonally cyclic equitable (r,c;v)-rectangle.

Original language	English
Pages (from-to)	551-569
Number of pages	19
Journal	Designs Codes and Cryptography
Volume	76
Issue number	3
DOIs	https://doi.org/10.1007/s10623-014-9977-x
Publication status	Published - 6 Sept 2015

Keywords

Equitable rectangle
Latin rectangle
Latin square
Orthogonal array

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AB - An equitable (r,c;v)-rectangle is an r×c matrix L=(lij) with symbols from (Formula presented.) in which each symbol appears in every row either (Formula presented.) or (Formula presented.) times and in every column either (Formula presented.) or (Formula presented.) times. We call L diagonally cyclic if l(i+1) (j+1)=lij+1, where the rows are indexed by (Formula presented.) and columns indexed by (Formula presented.). We give a constructive proof of necessary and sufficient conditions for the existence of a diagonally cyclic equitable (r,c;v)-rectangle.

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KW - Latin square

KW - Orthogonal array

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Diagonally cyclic equitable rectangles

Abstract

Keywords

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