The Andrews-Sellers family of partition congruences

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• 作者：Peter Paule ^{Peter.Paule@risc.uni-linz.ac.at} ; Cristian-Silviu Radu ; ^{Silviu.Radu@risc.uni-linz.ac.at} ; ^{sradu@risc.jku.at}
• 关键词：primary ; 11P83 ; secondary ; 05A17
• 刊名：Advances in Mathematics
• 出版年：2012
• 出版时间：20 June, 2012
• 年：2012
• 卷：230
• 期：3
• 页码：819-838
• 全文大小：232 K

文摘

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.