On the parity of generalized partition functions, III

Fethi Ben Saïd[1]; Jean-Louis Nicolas[2]; Ahlem Zekraoui[1]

  • [1] Université de Monastir Faculté des Sciences de Monastir Avenue de l’Environement 5000 Monastir, Tunisie
  • [2] Université de Lyon 1 Institut Camile Jordan, UMR 5208 Batiment Doyen Jean Braconnier 21 Avenue Claude Bernard F-69622 Villeurbanne, France

Journal de Théorie des Nombres de Bordeaux (2010)

  • Volume: 22, Issue: 1, page 51-78
  • ISSN: 1246-7405

Abstract

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Improving on some results of J.-L. Nicolas [15], the elements of the set 𝒜 = 𝒜 ( 1 + z + z 3 + z 4 + z 5 ) , for which the partition function p ( 𝒜 , n ) (i.e. the number of partitions of n with parts in 𝒜 ) is even for all n ≥ 6 are determined. An asymptotic estimate to the counting function of this set is also given.

How to cite

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Ben Saïd, Fethi, Nicolas, Jean-Louis, and Zekraoui, Ahlem. "On the parity of generalized partition functions, III." Journal de Théorie des Nombres de Bordeaux 22.1 (2010): 51-78. <http://eudml.org/doc/116400>.

@article{BenSaïd2010,
abstract = {Improving on some results of J.-L. Nicolas [15], the elements of the set $\{\mathcal\{A\}\}=\{\mathcal\{A\}\}(1+z+z^3+z^4+z^5)$, for which the partition function $p(\{\mathcal\{A\}\},n)$ (i.e. the number of partitions of $n$ with parts in $\{\mathcal\{A\}\}$) is even for all $n\ge 6$ are determined. An asymptotic estimate to the counting function of this set is also given.},
affiliation = {Université de Monastir Faculté des Sciences de Monastir Avenue de l’Environement 5000 Monastir, Tunisie; Université de Lyon 1 Institut Camile Jordan, UMR 5208 Batiment Doyen Jean Braconnier 21 Avenue Claude Bernard F-69622 Villeurbanne, France; Université de Monastir Faculté des Sciences de Monastir Avenue de l’Environement 5000 Monastir, Tunisie},
author = {Ben Saïd, Fethi, Nicolas, Jean-Louis, Zekraoui, Ahlem},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Partitions; periodic sequences; order of a polynomial; orbits; $2$-adic numbers; counting function; Selberg-Delange formula; partitions; 2-adic numbers; counting functions},
language = {eng},
number = {1},
pages = {51-78},
publisher = {Université Bordeaux 1},
title = {On the parity of generalized partition functions, III},
url = {http://eudml.org/doc/116400},
volume = {22},
year = {2010},
}

TY - JOUR
AU - Ben Saïd, Fethi
AU - Nicolas, Jean-Louis
AU - Zekraoui, Ahlem
TI - On the parity of generalized partition functions, III
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2010
PB - Université Bordeaux 1
VL - 22
IS - 1
SP - 51
EP - 78
AB - Improving on some results of J.-L. Nicolas [15], the elements of the set ${\mathcal{A}}={\mathcal{A}}(1+z+z^3+z^4+z^5)$, for which the partition function $p({\mathcal{A}},n)$ (i.e. the number of partitions of $n$ with parts in ${\mathcal{A}}$) is even for all $n\ge 6$ are determined. An asymptotic estimate to the counting function of this set is also given.
LA - eng
KW - Partitions; periodic sequences; order of a polynomial; orbits; $2$-adic numbers; counting function; Selberg-Delange formula; partitions; 2-adic numbers; counting functions
UR - http://eudml.org/doc/116400
ER -

References

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