Counting acyclic and strong digraphs by descents
Discrete Mathematics(2020)
摘要
A descent of a labeled digraph is a directed edge (s,t) with s>t. We count strong tournaments, strong digraphs, acyclic digraphs, and forests by descents and edges. To count strong tournaments we use Eulerian generating functions and to count strong and acyclic digraphs we use a new type of generating function that we call a graphic Eulerian generating function.
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关键词
Acyclic digraph,Strong digraph,Strong tournament,Descent,Eulerian generating function,Graphic generating function
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