蛛网偏序集和KoDAG有向图表示关系的自然并及其diBigraphs和相应的邻接矩阵
Cobweb Posets and KoDAG Digraphs are Representing Natural Join of Relations, their diBigraphs and the Corresponding Adjacency Matrices
摘要：
定义了有向二部图$di-bigraphs$及其邻接矩阵的自然并，并将其应用于研究蛛网偏序集及其$Hasse$有向图$KoDAGs$ . $KoDAGs$是作者在几年前引入的一类特殊的可序有向无圈图，它是蛛网偏序集的覆盖关系有向图。$KoDAGs$是$Ferrers$有向图族中的一个特殊族，它是由一个单向团$di-bicliques$组成的有序链的自然并.这些有向图用来忠实地表示任意元的对应关系，使得任意元的所有关系都是它们的子关系。作为这$chain -way$完成，如果与kompletne $Kuratowski$二部图相比，其$DAG$表示伴随着字母$K$前面的描述性缩写$oDAG$。将二元二部有向图连接成$multi-ary$关系的方法是对关系或其有向图表示进行自然连接操作。这种自然连接操作在这里由$\os$符号表示，故意指邻接矩阵的直接和$\oplus$，因为它变成了不相交的$di-bigraphs$的情况。
英文摘要：
Natural join of $di-bigraphs$ that is directed biparted graphs and their corresponding adjacency matrices is defined and then applied to investigate the so called cobweb posets and their $Hasse$ digraphs called $KoDAGs$. $KoDAGs$ are special orderable directed acyclic graphs which are cover relation digraphs of cobweb posets introduced by the author few years ago. $KoDAGs$ appear to be distinguished family of $Ferrers$ digraphs which are natural join of a corresponding ordering chain of one direction directed cliques called $di-bicliques$. These digraphs serve to represent faithfully corresponding relations of arbitrary arity so that all relations of arbitrary arity are their subrelations. Being this $chain -way$ complete if compared with kompletne $Kuratowski$ bipartite graphs their $DAG$ denotation is accompanied with the letter $K$ in front of descriptive abbreviation $oDAG$. The way to join bipartite digraphs of binary into $multi-ary$ relations is the natural join operation either on relations or their digraph representatives. This natural join operation is denoted here by $\os$ symbol deliberately referring to the direct sum $\oplus$ of adjacency matrices as it becomes the case for disjoint $di-bigraphs$.
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