On recurrences of Fahr and Ringel arising in graph theory.
Hirschhorn, Michael D. (2009)
Journal of Integer Sequences [electronic only]
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Hirschhorn, Michael D. (2009)
Journal of Integer Sequences [electronic only]
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Benito, Manuel, Creyaufmüller, Wolfgang, Varona, Juan L., Zimmermann, Paul (2002)
Experimental Mathematics
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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.
Kimberling, Clark (2007)
Journal of Integer Sequences [electronic only]
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Pinthira Tangsupphathawat, Narong Punnim, Vichian Laohakosol (2012)
Colloquium Mathematicae
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The problem whether each element of a sequence satisfying a fourth order linear recurrence with integer coefficients is nonnegative, referred to as the Positivity Problem for fourth order linear recurrence sequence, is shown to be decidable.
Cossali, G.E. (2003)
Journal of Integer Sequences [electronic only]
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Moree, Pieter (2004)
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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Diego Marques, Alain Togbé (2011)
Colloquium Mathematicae
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In 2000, Florian Luca proved that F₁₀ = 55 and L₅ = 11 are the largest numbers with only one distinct digit in the Fibonacci and Lucas sequences, respectively. In this paper, we find terms of a linear recurrence sequence with only one block of digits in its expansion in base g ≥ 2. As an application, we generalize Luca's result by finding the Fibonacci and Lucas numbers with only one distinct block of digits of length up to 10 in its decimal expansion.
Emerson, Nathaniel D. (2006)
Journal of Integer Sequences [electronic only]
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Hans Carstens (1975)
Fundamenta Mathematicae
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Hiroyuki Okazaki (2015)
Formalized Mathematics
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In this article we formalize negligible functions that play an essential role in cryptology [10], [2]. Generally, a cryptosystem is secure if the probability of succeeding any attacks against the cryptosystem is negligible. First, we formalize the algebra of polynomially bounded sequences [20]. Next, we formalize negligible functions and prove the set of negligible functions is a subset of the algebra of polynomially bounded sequences. Moreover, we then introduce equivalence relation...