论文标题
适用于$ k $的平面平面分区和可划分的本地化方法5
The Localization Method Applied to $k$-Elongated Plane Partitions and Divisibility by 5
论文作者
论文摘要
$ k $的枚举$ d_k（n）$ eLogend的平面钻石钻石已成为经典整数分区函数$ p（n）$的概括。我们发现了一个无限的一致性家族，$ d_5（n）$ MODULO PAWERS 5。无法使用经典方法来证明这个一致的一流。的确，该证明采用了最近开发的本地化方法，并利用了惊人的内部代数结构，该结构尚未在任何一致家族的证据中看到。我们认为，这一发现对分区一致性的未来工作产生了重要意义。
The enumeration $d_k(n)$ of $k$-elongated plane partition diamonds has emerged as a generalization of the classical integer partition function $p(n)$. We have discovered an infinite congruence family for $d_5(n)$ modulo powers of 5. Classical methods cannot be used to prove this family of congruences. Indeed, the proof employs the recently developed localization method, and utilizes a striking internal algebraic structure which has not yet been seen in the proof of any congruence family. We believe that this discovery poses important implications on future work in partition congruences.
