Families of linear recurrences for Catalan numbers

2011 ◽  
Vol 42 (1) ◽  
pp. 131-139 ◽  
Author(s):  
N. Gauthier
Keyword(s):  
Catalan Numbers ◽  
Linear Recurrences

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.

scholarly journals ON THE GROWTH OF LINEAR RECURRENCES IN FUNCTION FIELDS

2020 ◽  
pp. 1-10
Author(s):  
CLEMENS FUCHS ◽  
SEBASTIAN HEINTZE
Keyword(s):  
Number Field ◽  
Function Field ◽  
Function Fields ◽  
Linear Recurrence ◽  
Recurrence Sequence ◽  
Linear Recurrences ◽  
Field Case ◽  
Power Sum ◽  
Linear Recurrence Sequence

Abstract Let $ (G_n)_{n=0}^{\infty } $ be a nondegenerate linear recurrence sequence whose power sum representation is given by $ G_n = a_1(n) \alpha _1^n + \cdots + a_t(n) \alpha _t^n $ . We prove a function field analogue of the well-known result in the number field case that, under some nonrestrictive conditions, $ |{G_n}| \geq ( \max _{j=1,\ldots ,t} |{\alpha _j}| )^{n(1-\varepsilon )} $ for $ n $ large enough.

scholarly journals Automatic Hierarchical Parallelization of Linear Recurrences

2018 ◽  
Vol 53 (2) ◽  
pp. 128-138
Author(s):  
Sepideh Maleki ◽  
Martin Burtscher
Keyword(s):  
Linear Recurrences

scholarly journals ON DIVISIBILITY OF BINOMIAL COEFFICIENTS

2012 ◽  
Vol 93 (1-2) ◽  
pp. 189-201 ◽  
Author(s):  
ZHI-WEI SUN
Keyword(s):  
Higher Order ◽  
Catalan Numbers ◽  
Binomial Coefficients

AbstractIn this paper, motivated by Catalan numbers and higher-order Catalan numbers, we study factors of products of at most two binomial coefficients.

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