Generalized Beatty sequences.
Mercer, A.McD. (1978)
International Journal of Mathematics and Mathematical Sciences
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Mercer, A.McD. (1978)
International Journal of Mathematics and Mathematical Sciences
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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.
Noe, Tony D., Vos Post, Jonathan (2005)
Journal of Integer Sequences [electronic only]
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Faure, Henri (2005)
Integers
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Henri Faure (2005)
Acta Arithmetica
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Hans Carstens (1975)
Fundamenta Mathematicae
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C. Zaremba (1963)
Applicationes Mathematicae
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Gould, H.W., Quaintance, Jocelyn (2007)
Integers
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Henri Faure, Christiane Lemieux (2016)
Acta Arithmetica
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Sobol' sequences are a popular family of low-discrepancy sequences, in spite of requiring primitive polynomials instead of irreducible ones in later constructions by Niederreiter and Tezuka. We introduce a generalization of Sobol' sequences that removes this shortcoming and that we believe has the potential of becoming useful for practical applications. Indeed, these sequences preserve two important properties of the original construction proposed by Sobol': their generating matrices...
Bóna, Miklós, Sagan, Bruce E. (2005)
Journal of Integer Sequences [electronic only]
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Lenny Jones (2012)
Acta Arithmetica
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Jovan D. Kečkić (1973)
Publications de l'Institut Mathématique
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Kimberling, Clark (2007)
Journal of Integer Sequences [electronic only]
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