论文标题
扭曲分区的一致性分类
Classification of congruences of twisted partition monoids
论文作者
论文摘要
扭曲的分区单差$ \ MATHCAL {p} _n^φ$是一种从经典有限分区单独的$ \ Mathcal {p} _n $获得的无限单型，它通过考虑到乘以分区时的浮动组件数量。本文的主要结果是对$ \ Mathcal {p} _n^φ$的一致性的完整描述。我们称之为c-pair的简洁编码由$ n+1 $ Qualtences的序列组成。我们还描述了按照c对的词典样订购的序列的包含顺序。然后，将其用于对有限$ D $ twist的分区$ \ Mathcal {p} _ {n，d}^φ$进行分类，这些分区是通过从$ \ Mathcal {p} _n^φ$中算出来的所有分区的所有分区的理想来获得的。我们结果的进一步应用，阐明了（$ d $ - ）扭曲的分区单体的一致性晶格的结构和属性，这将是未来文章的主题。
The twisted partition monoid $\mathcal{P}_n^Φ$ is an infinite monoid obtained from the classical finite partition monoid $\mathcal{P}_n$ by taking into account the number of floating components when multiplying partitions. The main result of this paper is a complete description of the congruences on $\mathcal{P}_n^Φ$. The succinct encoding of a congruence, which we call a C-pair, consists of a sequence of $n+1$ congruences on the additive monoid $\mathbb{N}$ of natural numbers and a certain $(n+1)\times\mathbb{N}$ matrix. We also give a description of the inclusion ordering of congruences in terms of a lexicographic-like ordering on C-pairs. This is then used to classify congruences on the finite $d$-twisted partition monoids $\mathcal{P}_{n,d}^Φ$, which are obtained by factoring out from $\mathcal{P}_n^Φ$ the ideal of all partitions with more than $d$ floating components. Further applications of our results, elucidating the structure and properties of the congruence lattices of the ($d$-)twisted partition monoids, will be the subject of a future article.
