Partitioning the positive integers with higher order recurrences
1991 ◽
Vol 14
(3)
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pp. 457-462
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Keyword(s):
Associated with any irrational numberα>1and the functiong(n)=[αn+12]is an array{s(i,j)}of positive integers defined inductively as follows:s(1,1)=1,s(1,j)=g(s(1,j−1))for allj≥2,s(i,1)=the least positive integer not amongs(h,j)forh≤i−1fori≥2, ands(i,j)=g(s(i,j−1))forj≥2. This work considers algebraic integersαof degree≥3for which the rows of the arrays(i,j)partition the set of positive integers. Such an array is called a Stolarsky array. A typical result is the following (Corollary 2): ifαis the positive root ofxk−xk−1−…−x−1fork≥3, thens(i,j)is a Stolarsky array.
1961 ◽
Vol 5
(1)
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pp. 35-40
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2018 ◽
Vol 11
(04)
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pp. 1850056
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Keyword(s):
2021 ◽
Vol 14
(2)
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pp. 380-395
2009 ◽
Vol DMTCS Proceedings vol. AK,...
(Proceedings)
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2015 ◽
Vol DMTCS Proceedings, 27th...
(Proceedings)
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2005 ◽
Vol 01
(04)
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pp. 563-581
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