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The Palindrome Concept and Its Applications to Prime Numbers [PDF]
, 2006 This article originates from a proposal by M. L. Perez of American Research Press to carry out a study on Smarandache generalized palindromes [1]. The prime numbers were chosen as a rst set of numbers to apply the development of ideas and computer ...
Ibstedt, H.
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Generalized Thue-Morse words and palindromic richness [PDF]
, 2011 We prove that the generalized Thue-Morse word $\mathbf{t}_{b,m}$ defined for $b \geq 2$ and $m \geq 1$ as $\mathbf{t}_{b,m} = (s_b(n) \mod m)_{n=0}^{+\infty}$, where $s_b(n)$ denotes the sum of digits in the base-$b$ representation of the integer $n ...
Starosta, Štěpán
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Palindromic complexity of infinite words associated with simple Parry numbers [PDF]
, 2006 A simple Parry number is a real number \beta>1 such that the R\'enyi expansion of 1 is finite, of the form d_\beta(1)=t_1...t_m. We study the palindromic structure of infinite aperiodic words u_\beta that are the fixed point of a substitution associated ...
Ambrož, Petr +3 more
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Enumeration and Structure of Trapezoidal Words [PDF]
, 2012 Trapezoidal words are words having at most $n+1$ distinct factors of length $n$ for every $n\ge 0$. They therefore encompass finite Sturmian words. We give combinatorial characterizations of trapezoidal words and exhibit a formula for their enumeration ...
Alessandro De Luca +21 more
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Palindromes in infinite ternary words [PDF]
, 2009 We study infinite words u over an alphabet A satisfying the property P : P(n)+ P(n+1) = 1+ #A for any n in N, where P(n) denotes the number of palindromic factors of length n occurring in the language of u.
Balkova, Lubomira +2 more
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Palindromic Bernoulli distributions [PDF]
Electronic Journal of Statistics, 2016 17 pages, 1 figure, 5 ...
MARCHETTI, GIOVANNI MARIA +1 more
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Palindromes in Different Bases: A Conjecture of J. Ernest Wilkins
, 2009 We show that there exist exactly 203 positive integers $N$ such that for some integer $d \geq 2$ this number is a $d$-digit palindrome base 10 as well as a $d$-digit palindrome for some base $b$ different from 10.
Goins, Edray Herber
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Extensions of rich words [PDF]
, 2013 In [X. Droubay et al, Episturmian words and some constructions of de Luca and Rauzy, Theoret. Comput. Sci. 255 (2001)], it was proved that every word w has at most |w|+1 many distinct palindromic factors, including the empty word.
Vesti, Jetro
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v-Palindromes: an Analogy to the Palindromes
The PUMP Journal of Undergraduate ResearchAround the year 2007, one of the authors, Tsai, accidentally discovered a property of the number 198 he saw on the license plate of a car. Namely, if we take 198 and its reversal 891, which have prime factorizations 198 = 2 · 32 · 11 and 891 = 34 · 11 respectively, and sum the numbers appearing in each factorization getting 2 + 3 + 2 + 11 = 18 and 3 ...
Bispels, Chris +4 more
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