关于超图和超块的计数公式

摘要

主要研究超图的若干计数问题,分别给出一般的及连通的(p ,q )超图、p 阶超图、无环(p ,q )超图、无环 p 阶超图、匀称 k 秩(p ,q )超图和匀称 k 秩 p 阶超图的计数公式,并建立超块与连通无环超图其指数生成函数的关系式,进而获得超块的递推计数公式。%In this paper,some problems about enumeration of hypergraphs are studied.On one hand, we present the counting formulas for (connected)(p ,q )-hypergraphs,hypergraphs of order p ,loop-free (p ,q )-hypergraphs,loop-free hypergraphs of order p , k-uniform (p ,q )-hypergraphs,k-uniform hypergraphs of order p ,respectively;on the other hand,the relation between the exponential generating functions for hyperblocks and connected loop-free hypergraphs is established,and the recursive counting formula of hyperblocks is obtained.