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The Andrews–Sellers family of partition congruences
Advances in Mathematics ( IF 1.7 ) Pub Date : 2012-06-01 , DOI: 10.1016/j.aim.2012.02.026
Peter Paule 1 , Cristian-Silviu Radu
Affiliation  

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.

中文翻译:

划分同余的 Andrews-Sellers 族

1994 年,James Sellers 为 George E. Andrews 引入的 2 色 Frobenius 分区推测了一个无限的 Ramanujan 类型同余族。这些同余产生了 5 的模幂。 2002 年,丹尼斯·艾希霍恩 (Dennis Eichhorn) 和塞勒斯 (Sellers) 能够解决最多 4 次幂的猜想。在本文中,我们证明塞勒斯 (Sellers) 对 5 的所有幂的猜想。此外,我们讨论了为什么安德鲁斯——塞勒斯族与素数的经典同余模幂有显着不同。
更新日期:2012-06-01
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