Enumeration in musical theory.

Fripertinger, Harald

Displaying similar documents to “Enumeration in musical theory.”

Excedance numbers for permutations in complex reflection groups.

Mansour, Toufik, Sun, Yidong (2007)

Séminaire Lotharingien de Combinatoire [electronic only]

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On the excedance number of colored permutation groups.

Bagno, Eli, Garber, David (2005)

Séminaire Lotharingien de Combinatoire [electronic only]

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Primes, permutations and primitive roots.

Lewittes, Joseph, Kolyvagin, Victor (2010)

The New York Journal of Mathematics [electronic only]

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Pattern avoidance in coloured permutations.

Mansour, Toufik (2001)

Séminaire Lotharingien de Combinatoire [electronic only]

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Fibonacci numbers and Fermat's last theorem

Zhi-Wei Sun (1992)

Acta Arithmetica

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Let Fₙ be the Fibonacci sequence defined by F₀=0, F₁=1, $F_{n + 1} = F ₙ + F_{n - 1} (n \geq 1)$ . It is well known that $F_{p - (5 / p)} \equiv 0 (m o d p)$ for any odd prime p, where (-) denotes the Legendre symbol. In 1960 D. D. Wall [13] asked whether $p ² | F_{p - (5 / p)}$ is always impossible; up to now this is still open. In this paper the sum $\sum_{k \equiv r (m o d 10)} (\binom{n}{k})$ is expressed in terms of Fibonacci numbers. As applications we obtain a new formula for the Fibonacci quotient $F_{p - (5 / p)} / p$ and a criterion for the relation $p | F_{(p - 1) / 4}$ (if p ≡ 1 (mod 4), where p ≠ 5 is an odd prime. We also prove that the affirmative...

On the number of representations of positive integers by the quadratic form $x_{1}^{2} + \dots + x_{8}^{2} + 4 x_{9}^{2}$ .

Lomadze, G. (2001)

Georgian Mathematical Journal

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On integers not of the form n - φ (n)

J. Browkin, A. Schinzel (1995)

Colloquium Mathematicae

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W. Sierpiński asked in 1959 (see [4], pp. 200-201, cf. [2]) whether there exist infinitely many positive integers not of the form n - φ(n), where φ is the Euler function. We answer this question in the affirmative by proving Theorem. None of the numbers $2^{k} \cdot 509203$ (k = 1, 2,...) is of the form n - φ(n).

The diophantine equation x² + 19 = yⁿ

J. H. E. Cohn (1992)

Acta Arithmetica

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On the parity of generalized partition functions, III

Fethi Ben Saïd, Jean-Louis Nicolas, Ahlem Zekraoui (2010)

Journal de Théorie des Nombres de Bordeaux

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Improving on some results of J.-L. Nicolas [], the elements of the set $𝒜 = 𝒜 (1 + z + z^{3} + z^{4} + z^{5})$ , for which the partition function $p (𝒜, n)$ (i.e. the number of partitions of $n$ with parts in $𝒜$ ) is even for all $n \geq 6$ are determined. An asymptotic estimate to the counting function of this set is also given.

Cyclic partitions of complete uniform hypergraphs.

Szymanski, Artur, Wojda, A.Paweł (2010)

The Electronic Journal of Combinatorics [electronic only]

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