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https://hdl.handle.net/10119/4923
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| Title: | A Generalization of Magic Squares with Applications to Digital Halftoning |
| Authors: | Aronov, Boris
Asano, Tetsuo
Kikuchi, Yosuke
Nandy, Subhas C.
Sasahara, Shinji
Uno, Takeaki |
| Keywords: | digital halftoning
discrepancy
latin square
magic square
matrix |
| Issue Date: | 2008-02 |
| Publisher: | Springer |
| Magazine name: | Theory of Computing Systems |
| Volume: | 42 |
| Number: | 2 |
| Start page: | 143 |
| End page: | 156 |
| DOI: | 10.1007/s00224-007-9005-x |
| Abstract: | A semimagic square of order n is an n × n matrix containing the integers 0,…,n^2 _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 × k-discrepancy 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 relatively prime. Further, the existence is also guaranteed whenever n = k^m, 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. |
| Rights: | This is the author-created version of Springer, Boris Aronov, Tetsuo Asano, Yosuke Kikuchi, Subhas C. Nandy, Shinji Sasahara and Takeaki Uno, Theory of Computing Systems, 42(2), 2008, 143-156. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/s00224-007-9005-x |
| URI: | https://hdl.handle.net/10119/4923 |
| Material Type: | author |
| Appears in Collections: | b10-1. 雑誌掲載論文 (Journal Articles)
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