Complementary equations.
Kimberling, Clark (2007)
Journal of Integer Sequences [electronic only]
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Kimberling, Clark (2007)
Journal of Integer Sequences [electronic only]
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Mullen, Ryan (2009)
Journal of Integer Sequences [electronic only]
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Mauro Torelli (2006)
RAIRO - Theoretical Informatics and Applications
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Increasing integer sequences include many instances of interesting sequences and combinatorial structures, ranging from tournaments to addition chains, from permutations to sequences having the that any integer greater than 1 can be obtained as the sum of two elements in the sequence. The paper introduces and compares several of these classes of sequences, discussing recurrence relations, enumerative problems and questions concerning shortest sequences.
Cossali, G.E. (2003)
Journal of Integer Sequences [electronic only]
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Mercer, A.McD. (1978)
International Journal of Mathematics and Mathematical Sciences
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Šuník, Zoran (2002)
Journal of Integer Sequences [electronic only]
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Kimberling, Clark (1991)
International Journal of Mathematics and Mathematical Sciences
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Faure, Henri (2005)
Integers
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Kimberling, Clark (2008)
Journal of Integer Sequences [electronic only]
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Vinh, Le Anh (2007)
Journal of Integer Sequences [electronic only]
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Adams-Watters, Franklin T., Ruskey, Frank (2009)
Journal of Integer Sequences [electronic only]
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Artur Bartoszewicz, Małgorzata Filipczak, Emilia Szymonik (2014)
Open Mathematics
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For a sequence x ∈ l 10, one can consider the achievement set E(x) of all subsums of series Σn=1∞ x(n). It is known that E(x) has one of the following structures: a finite union of closed intervals, a set homeomorphic to the Cantor set, a set homeomorphic to the set T of subsums of Σn=1∞ x(n) where c(2n − 1) = 3/4n and c(2n) = 2/4n (Cantorval). Based on ideas of Jones and Velleman [Jones R., Achievement sets of sequences, Amer. Math. Monthly, 2011, 118(6), 508–521] and Guthrie and Nymann...