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math.CO2023
On a conjecture of Knuth about forward and back arcs
Zipei Nie
Following Janson's method, we prove a conjecture of Knuth: the numbers of forward and back arcs for the depth-first search (DFS) in a digraph with a geometric outdegree distributio…
math.CO2014
Hilbert Functions and the Finite Degree Zariski Closure in Finite Field Combinatorial Geometry
Zipei Nie, Anthony Y. Wang
The polynomial method has been used recently to obtain many striking results in combinatorial geometry. In this paper, we use affine Hilbert functions to obtain an estimation theor…