Year: 2017
Type: preprint
Abstract: We consider labeled $r$-uniform hypertrees having $n \ge r \ge 2$ vertices. The number of hyperedges in such a hypertree is $m = (n - 1)/(r - 1)$. We show that there are exactly $f(n, r) = \frac{(n-1)! n^{m-1}}{(r-1)!^m m!}$ $r$-uniform hypertrees with $n$ vertices labeled with distinct integers. We also give an encoding scheme that encodes such hypertrees using, on an average, at most $1 + \log_2 e$ bits more than $\log_2(f(n, r))$.
Source: arXiv (Cornell University)
Authors: Pitchanathan, Arjun, Shannigrahi, Saswata
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2767890042