scholarly journals Conditions for the algebraic independence of certain series involving continued fractions and generated by linear recurrences

2009 ◽  
Vol 129 (12) ◽  
pp. 3081-3093
Author(s):  
Taka-aki Tanaka
Keyword(s):  
Continued Fractions ◽  
Algebraic Independence ◽  
Linear Recurrences

scholarly journals Continued fractions and linear recurrences

1993 ◽  
Vol 61 (203) ◽  
pp. 351-351 ◽  
Author(s):  
H. W. Lenstra ◽  
J. O. Shallit
Keyword(s):  
Continued Fractions ◽  
Linear Recurrences

Linear recurrences associated to rays in Pascal’s triangle and combinatorial identities

2014 ◽  
Vol 64 (2) ◽  
Author(s):  
Hacène Belbachir ◽  
Takao Komatsu ◽  
László Szalay
Keyword(s):  
Recurrence Relation ◽  
Generating Function ◽  
Finite Differences ◽  
Continued Fractions ◽  
Fibonacci Numbers ◽  
Combinatorial Identities ◽  
Bivariate Polynomials ◽  
Linear Recurrences ◽  
Pascal’S Triangle ◽  
Pascal's Triangle

AbstractOur main purpose is to describe the recurrence relation associated to the sum of diagonal elements laying along a finite ray crossing Pascal’s triangle. We precise the generating function of the sequence of described sums. We also answer a question of Horadam posed in his paper [Chebyshev and Pell connections, Fibonacci Quart. 43 (2005), 108–121]. Further, using Morgan-Voyce sequence, we establish the nice identity $F_{n + 1} - iF_n = i^n \sum\limits_{k = 0}^n {(_{2k}^{n + k} )( - 2 - i)^k } $ of Fibonacci numbers, where i is the imaginary unit. Finally, connections to continued fractions, bivariate polynomials and finite differences are given.

CLASS OF BOOLEAN FUNCTIONS CONSTRUCTED USING SIGNIFICANT BITS OF LINEAR RECURRENCES OVER THE RING ℤ2n

2019 ◽  
Vol 6 (2) ◽  
pp. 90-94
Author(s):  
Hernandez Piloto Daniel Humberto
Keyword(s):  
Linear Function ◽  
Boolean Functions ◽  
Hamming Distance ◽  
Linear Recurrences ◽  
Maximum Period ◽  
Non Linear ◽  
The Given ◽  
Class Of Functions

In this work a class of functions is studied, which are built with the help of significant bits sequences on the ring ℤ2n. This class is built with use of a function ψ: ℤ2n → ℤ2. In public literature there are works in which ψ is a linear function. Here we will use a non-linear ψ function for this set. It is known that the period of a polynomial F in the ring ℤ2n is equal to T(mod 2)2α, where α∈ , n01- . The polynomials for which it is true that T(F) = T(F mod 2), in other words α = 0, are called marked polynomials. For our class we are going to use a polynomial with a maximum period as the characteristic polyomial. In the present work we show the bounds of the given class: non-linearity, the weight of the functions, the Hamming distance between functions. The Hamming distance between these functions and functions of other known classes is also given.

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