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p-adic valuations of some sums of multinomial coefficients

Zhi-Wei Sun (2011)

Acta Arithmetica

p-adische Kettenbrüche und Irrationalität p-adischer Zahlen.

P. Bundschuh (1977)

Elemente der Mathematik

Palindromes in different bases: a conjecture of J. Ernest Wilkins.

Goins, Edray Herber (2009)

Integers

Palindromic complexity of infinite words associated with non-simple Parry numbers

L'ubomíra Balková, Zuzana Masáková (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We study the palindromic complexity of infinite words $u_{β}$ , the fixed points of the substitution over a binary alphabet, $ϕ (0) = 0^{a} 1$ , $ϕ (1) = 0^{b} 1$ , with $a - 1 \geq b \geq 1$ , which are canonically associated with quadratic non-simple Parry numbers $β$ .

Palindromic complexity of infinite words associated with non-simple Parry numbers

L'ubomíra Balková, Zuzana Masáková (2008)

RAIRO - Theoretical Informatics and Applications

We study the palindromic complexity of infinite words uβ, the fixed points of the substitution over a binary alphabet, φ(0) = 0a1, φ(1) = 0b1, with a - 1 ≥ b ≥ 1, which are canonically associated with quadratic non-simple Parry numbers β.

Palindromic complexity of infinite words associated with simple Parry numbers

Petr Ambrož, Zuzana Masáková, Edita Pelantová, Christiane Frougny (2006)

Annales de l’institut Fourier

A simple Parry number is a real number $β > 1$ such that the Rényi expansion of $1$ is finite, of the form $d_{β} (1) = t_{1} \dots t_{m}$ . We study the palindromic structure of infinite aperiodic words $u_{β}$ that are the fixed point of a substitution associated with a simple Parry number $β$ . It is shown that the word $u_{β}$ contains infinitely many palindromes if and only if $t_{1} = t_{2} = \dots = t_{m - 1} \geq t_{m}$ . Numbers $β$ satisfying this condition are the so-called confluent Pisot numbers. If $t_{m} = 1$ then $u_{β}$ is an Arnoux-Rauzy word. We show that if $β$ is a confluent Pisot number then...

Palindromic squares for various number system bases

Ivan Korec (1991)

Mathematica Slovaca

Parry expansions of polynomial sequences.

Steiner, Wolfgang (2002)

Integers

Partial sums of powers of prime factors.

De Koninck, Jean-Marie, Luca, Florian (2007)

Journal of Integer Sequences [electronic only]

Partitioning multipartite numbers into a fixed number of parts which satisfy congruence conditions.

M.M. Robertson (1977)

Journal für die reine und angewandte Mathematik

Partitions in the prime number maze

Michael I. Hartley (2002)

Acta Arithmetica

Partitions quadratiques et cyclotomie

Philippe Barkan (1974/1975)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

Pascal's triangle (mod 9)

James G. Huard, Blair K. Spearman, Kenneth S. Williams (1997)

Acta Arithmetica

Pattern occurrence in the dyadic expansion of square root of two and an analysis of pseudorandom number generators.

Nuida, Koji (2010)

Integers

Pentagonal numbers in the Lucas sequence.

Luo, Ming (1996)

Portugaliae Mathematica

Perfect numbers and finite groups

Tom De Medts, Attila Maróti (2013)

Rendiconti del Seminario Matematico della Università di Padova

Perfect powers with all equal digits but one.

Kihel, Omar, Luca, Florian (2005)

Journal of Integer Sequences [electronic only]

Perfect, Semiperfect and Ore Numbers

Andreas Zachariou, Eleni Zachariou (1972)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Periodic expansions and units in quadratic and cubic number fields.

Charlotte Goryn Denenberg (1975)

Journal für die reine und angewandte Mathematik

Periodic Jacobi-Perron expansions associated with a unit

Brigitte Adam, Georges Rhin (2011)

Journal de Théorie des Nombres de Bordeaux

We prove that, for any unit $ϵ$ in a real number field $K$ of degree $n + 1$ , there exits only a finite number of n-tuples in $K^{n}$ which have a purely periodic expansion by the Jacobi-Perron algorithm. This generalizes the case of continued fractions for $n = 1$ . For $n = 2$ we give an explicit algorithm to compute all these pairs.

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