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N. Baccar Université de Monastir, Faculté des Sciences de Monastir, Département de Mathématiques Avenue de l'environnement, 5000, Monastir, Tunisie Avenue de l'environnement, 5000, Monastir, Tunisie

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F. Ben Sa?d Université de Monastir, Faculté des Sciences de Monastir, Département de Mathématiques Avenue de l'environnement, 5000, Monastir, Tunisie Avenue de l'environnement, 5000, Monastir, Tunisie

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A. Zekraoui Université de Monastir, Faculté des Sciences de Monastir, Département de Mathématiques Avenue de l'environnement, 5000, Monastir, Tunisie Avenue de l'environnement, 5000, Monastir, Tunisie

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## Summary

For PF2[z] with P(0)=1 and deg(P)≧ 1, let A =A(P) be the unique subset of  N (cf. [9]) such that Σn0 p(A,n)zn  ≡ P(z) mod 2, where p(A,n) is the number of partitions of n with parts in A. To determine the elements of the set A, it is important to consider the sequence σ(A,n) = Σ d|n, dAd, namely, the periodicity of the sequences (σ(A,2kn) mod 2k+1)n1 for all k ≧ 0 which was proved in [3]. In this paper, the values of such sequences will be given in terms of orbits. Moreover, a formula to σ(A,2kn) mod 2k+1 will be established, from which it will be shown that the weight σ(A1,2kzi) mod 2k+1    on the orbit \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $z_i$ \end{document} is moved on some other orbit zj when A1 is replaced by A2 with A1= A(P1) and A2= A(P2) P1 and P2 being irreducible in F2[z]  of the same odd order.

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder's
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Springer Nature Switzerland AG
Publisher's
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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