The Andrews–Sellers family of partition congruences

In 1994, James Sellers conjectured an infinite family of Ramanujan type congruences for 2-colored Frobenius partitions introduced by George E. Andrews. These congruences arise modulo powers of 5. In 2002 Dennis Eichhorn and Sellers were able to settle the conjecture for powers up to 4. In this artic...

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Detalles Bibliográficos
Autores principales: Paule, Peter, Radu, Cristian-Silviu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Academic Press 2012
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3587391/
https://www.ncbi.nlm.nih.gov/pubmed/23471147
http://dx.doi.org/10.1016/j.aim.2012.02.026
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author Paule, Peter
Radu, Cristian-Silviu
author_facet Paule, Peter
Radu, Cristian-Silviu
author_sort Paule, Peter
collection PubMed
description In 1994, James Sellers conjectured an infinite family of Ramanujan type congruences for 2-colored Frobenius partitions introduced by George E. Andrews. These congruences arise modulo powers of 5. In 2002 Dennis Eichhorn and Sellers were able to settle the conjecture for powers up to 4. In this article, we prove Sellers’ conjecture for all powers of 5. In addition, we discuss why the Andrews–Sellers family is significantly different from classical congruences modulo powers of primes.
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spelling pubmed-35873912013-03-05 The Andrews–Sellers family of partition congruences Paule, Peter Radu, Cristian-Silviu Adv Math (N Y) Article In 1994, James Sellers conjectured an infinite family of Ramanujan type congruences for 2-colored Frobenius partitions introduced by George E. Andrews. These congruences arise modulo powers of 5. In 2002 Dennis Eichhorn and Sellers were able to settle the conjecture for powers up to 4. In this article, we prove Sellers’ conjecture for all powers of 5. In addition, we discuss why the Andrews–Sellers family is significantly different from classical congruences modulo powers of primes. Academic Press 2012-06-20 /pmc/articles/PMC3587391/ /pubmed/23471147 http://dx.doi.org/10.1016/j.aim.2012.02.026 Text en © 2012 Elsevier Inc. https://creativecommons.org/licenses/by-nc-nd/3.0/ Open Access under CC BY-NC-ND 3.0 (https://creativecommons.org/licenses/by-nc-nd/3.0/) license
spellingShingle Article
Paule, Peter
Radu, Cristian-Silviu
The Andrews–Sellers family of partition congruences
title The Andrews–Sellers family of partition congruences
title_full The Andrews–Sellers family of partition congruences
title_fullStr The Andrews–Sellers family of partition congruences
title_full_unstemmed The Andrews–Sellers family of partition congruences
title_short The Andrews–Sellers family of partition congruences
title_sort andrews–sellers family of partition congruences
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3587391/
https://www.ncbi.nlm.nih.gov/pubmed/23471147
http://dx.doi.org/10.1016/j.aim.2012.02.026
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