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The number of N point digital discs

Huxley, Martin Neil and Žunić, Jovisa 2007. The number of N point digital discs. IEEE Transactions on Pattern Analysis and Machine Intelligence 29 (1) , pp. 159-161.

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A digital disc is the set of all integer points inside some given disc. Let {\cal D}_{N} be the number of different digital discs consisting of N points (different up to translation). The upper bound {\cal D}_{N} = {\cal O}(N^{2}) was shown recently; no corresponding lower bound is known. In this paper, we refine the upper bound to {\cal D}_{N} = {\cal O}(N), which seems to be the true order of magnitude, and we show that the average \overline{\cal D}_{N} = \left({\cal D}_{1} + {\cal D}_{2} + \ldots + {\cal D}_{N}\right)/N has upper and lower bounds which are of polynomial growth in N.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Institute of Electrical and Electronics Engineers
ISSN: 0162-8828
Last Modified: 04 Jun 2017 04:01

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