Wen-Nie W. J. Ma

On the limiting distribution of the number of improper edges for random trees

Improper edges were introduced by Shor to refine Cayley's formula for rooted labeled trees. Zeng established a connection between Shor's refinement and the Ramanujan polynomials. Let $\mathscr{T}_n$ denote the set of rooted labeled trees on $[n]=\{1,\ldots,n\}$. We prove that the number of improper edges in a uniformly...