\documentclass{article} \usepackage[utf8]{inputenc} \usepackage[small]{titlesec} \usepackage{fancybox} \usepackage{tikz} \newcommand{\Z}{{\sf Z}} \newcommand{\N}{{\sf N}} \newcommand{\Q}{{\sf Q}} \newcommand{\R}{{\sf R}} \newcommand{\Rpos}{{\sf R}^+} \newif{\ifshowsoln} \showsolntrue % comment out to NOT show solution inside \ifshowsoln and \fi blocks. \title{Honors Homework 8: \\ I think that I shall never see A HW lovely as a tree} \author{CMSC 250H} \date{Due Date: Monday April 12, 9:00AM, NO DEAD CAT } \begin{document} \maketitle In this HW you will do for 4-trees what was done in recitation for 3-trees. \begin{enumerate} \item Define a four-tree. \item Let $N(T)$ and $h(T)$ be as in recitation. State a theorem that bounds $N(T)$ by some function of $h(T)$. \item Prove your theorem. \end{enumerate} \end{document}