论文标题
通过FCA代表分区晶格
Representing partition lattices through FCA
论文作者
论文摘要
我们研究了标准上下文，由$ \ mathbb {k} \ left（\ Mathcal {l} _ {n} \ right）$，rattice $ \ mathcal {l} _ {l} _ {n} $ a $ n $ N $下的分区的分区$。受离散动力学模型的激励，以升级和钟进行整数分区，以及由Brylawski的$ n $的上述和（最不可还原）分区的表征，我们展示了如何构建$ \ \ \ \ \ \ \ \ \ n+1} $ n+n $ n $ n $ \ n $ \ n $ {l \ \ cancal-mathcal {l} $ {n $ {我们采用这种结构来计算$ \ Mathcal {l} _ {n} $的可结合元素的数量，并证明$ \ Mathbb {k} \ left（\ Mathcal {l} _ {l} _ {n} \右）$的对象（和属性）的数量（和属性）的数量。
We investigate the standard context, denoted by $\mathbb{K}\left(\mathcal{L}_{n}\right)$, of the lattice $\mathcal{L}_{n}$ of partitions of a positive integer $n$ under the dominance order. Motivated by the discrete dynamical model to study integer partitions by Latapy and Duong Phan and by the characterization of the supremum and (infimum) irreducible partitions of $n$ by Brylawski, we show how to construct the join-irreducible elements of $\mathcal{L}_{n+1}$ from $\mathcal{L}_{n}$. We employ this construction to count the number of join-irreducible elements of $\mathcal{L}_{n}$, and show that the number of objects (and attributes) of $\mathbb{K}\left(\mathcal{L}_{n}\right)$ has order $Θ(n^2)$.
