arXiv subjects

Xuming Liang

Publications and source records attributed to Xuming Liang.

2 recordsLinked to original sources

arXiv2020

Triangles with Vertices Equidistant to a Pedal Triangle

In this paper, we present a synthetic solution to a geometric open problem involving the radical axis of two strangely defined circumcircles. The solution encapsulates two generalizations, one of which uses a powerful projective result relating isogonal conjugation and polarity with respect to circumconics.

math.MG↗

arXiv2020

Counting acyclic and strong digraphs by descents

A descent of a labeled digraph is a directed edge (s, t) with s > t. We count strong tournaments, strong digraphs, and acyclic digraphs 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.

math.CO↗