Join Our Newsletter

Free Online Productivity Tools
i2Speak
i2Symbol
i2OCR
iTex2Img
iWeb2Print
iWeb2Shot
i2Type
iPdf2Split
iPdf2Merge
i2Bopomofo
i2Arabic
i2Style
i2Image
i2PDF
iLatex2Rtf
Sci2ools

ISAAC

2004

Springer

2004

Springer

A semimagic square of order n is an n ¢n matrix containing the integers 0 n2 1 arranged in such a way that each row and column add up to the same value. We generalize this notion to that of a zero k ¢kdiscrepancy matrix by replacing the requirement that the sum of each row and each column be the same by that of requiring that the sum of the entries in each k¢k square contiguous submatrix be the same. We show that such matrices exist if k and n are both even, and do not if k and n are are relatively prime. Further, the existence is also guaranteed whenever n km, for some integers k m 2. We present a space-efﬁcient algorithm for constructing such a matrix. Another class that we call constant-gap matrices arises in this construction. We give a characterization of such matrices. An application to digital halftoning is also mentioned.

Related Content

Added |
02 Jul 2010 |

Updated |
02 Jul 2010 |

Type |
Conference |

Year |
2004 |

Where |
ISAAC |

Authors |
Boris Aronov, Tetsuo Asano, Yosuke Kikuchi, Subhas C. Nandy, Shinji Sasahara, Takeaki Uno |

Comments (0)