scholarly journals On the Pseudorandomness of the Liouville Function of Polynomials over a Finite Field

2016 ◽  
Vol 11 (1) ◽  
pp. 47-58
Author(s):  
László Mérai ◽  
Arne Winterhof
Keyword(s):  
Finite Field ◽  
Linear Complexity ◽  
Möbius Function ◽  
Correlation Measure ◽  
Liouville Function ◽  
Mobius Function ◽  
Linear Complexity Profile

AbstractWe study several pseudorandom properties of the Liouville function and the Möbius function of polynomials over a finite field. More precisely, we obtain bounds on their balancedness as well as their well-distribution measure, correlation measure, and linear complexity profile.

scholarly journals The autocorrelation of the Möbius function and Chowla's conjecture for the rational function field in characteristic 2

2015 ◽  
Vol 373 (2040) ◽  
pp. 20140311 ◽  
Author(s):  
Dan Carmon
Keyword(s):  
Finite Field ◽  
Rational Function ◽  
Function Field ◽  
Möbius Function ◽  
Rational Function Field ◽  
Mobius Function ◽  
Characteristic 2

We prove a function field version of Chowla's conjecture on the autocorrelation of the Möbius function in the limit of a large finite field of characteristic 2, extending previous work in odd characteristic.

scholarly journals A Pseudorandom Sequence Generated over a Finite Field Using The Möbius Function

2021 ◽  
Vol 2 (1) ◽  
pp. 36-42
Author(s):  
Václav Zvoníček
Keyword(s):  
Finite Field ◽  
Randomized Algorithms ◽  
Main Part ◽  
Möbius Function ◽  
Pseudorandom Sequence ◽  
Pseudorandom Generator ◽  
Mobius Function

The aim of this paper is to generate and examine a pseudorandom sequence over a finite field using the Möbius function. In the main part of the paper, after generating a number of sequences using the Möbius function, we examine the sequences’ pseudorandomness using autocorrelation and prove that the second half of any sequence in $\mathbb{F}_{3^n}$ is the same as the first, but for the sign of the terms. I reach the conclusion, that it is preferable to generate sequences in fields of the form $\mathbb{F}_{3^n}$, thereby obtaining a sequence of the numbers $-1$,$0$,$1$, each of which appear in the same amounts. There is a variety of applications of the discussed pseudorandom generator and other generators such as cryptography or randomized algorithms.

Linear complexity profile and correlation measure of interleaved sequences

2015 ◽  
Vol 7 (4) ◽  
pp. 497-508 ◽  
Author(s):  
Jing Jane He ◽  
Daniel Panario ◽  
Qiang Wang ◽  
Arne Winterhof
Keyword(s):  
Linear Complexity ◽  
Correlation Measure ◽  
Linear Complexity Profile

ADJACENCY AND DEGREE OF GRAPH OF MOBIUS FUNCTION

2016 ◽  
Vol 5 (1) ◽  
pp. 31
Author(s):  
SRIMITRA K.K ◽  
BHARATHI D ◽  
SAJANA SHAIK ◽  
◽  
◽  
...  
Keyword(s):  
Möbius Function ◽  
Mobius Function

scholarly journals Enumerative Combinatorics of Intervals in the Dyck Pattern Poset

Order ◽  
2021 ◽  
Author(s):  
Antonio Bernini ◽  
Matteo Cervetti ◽  
Luca Ferrari ◽  
Einar Steingrímsson
Keyword(s):  
Möbius Function ◽  
Dyck Path ◽  
Enumerative Combinatorics ◽  
Closed Expression ◽  
Mobius Function ◽  
First Results ◽  
Two Peaks

AbstractWe initiate the study of the enumerative combinatorics of the intervals in the Dyck pattern poset. More specifically, we find some closed formulas to express the size of some specific intervals, as well as the number of their covering relations. In most of the cases, we are also able to refine our formulas by rank. We also provide the first results on the Möbius function of the Dyck pattern poset, giving for instance a closed expression for the Möbius function of initial intervals whose maximum is a Dyck path having exactly two peaks.

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