Skip to main content
\(\newcommand{\set}[1]{\{1,2,\dotsc,#1\,\}} \newcommand{\ints}{\mathbb{Z}} \newcommand{\posints}{\mathbb{N}} \newcommand{\rats}{\mathbb{Q}} \newcommand{\reals}{\mathbb{R}} \newcommand{\complexes}{\mathbb{C}} \newcommand{\twospace}{\mathbb{R}^2} \newcommand{\threepace}{\mathbb{R}^3} \newcommand{\dspace}{\mathbb{R}^d} \newcommand{\nni}{\mathbb{N}_0} \newcommand{\nonnegints}{\mathbb{N}_0} \newcommand{\dom}{\operatorname{dom}} \newcommand{\ran}{\operatorname{ran}} \newcommand{\prob}{\operatorname{prob}} \newcommand{\Prob}{\operatorname{Prob}} \newcommand{\height}{\operatorname{height}} \newcommand{\width}{\operatorname{width}} \newcommand{\length}{\operatorname{length}} \newcommand{\crit}{\operatorname{crit}} \newcommand{\inc}{\operatorname{inc}} \newcommand{\HP}{\mathbf{H_P}} \newcommand{\HCP}{\mathbf{H^c_P}} \newcommand{\GP}{\mathbf{G_P}} \newcommand{\GQ}{\mathbf{G_Q}} \newcommand{\AG}{\mathbf{A_G}} \newcommand{\GCP}{\mathbf{G^c_P}} \newcommand{\PXP}{\mathbf{P}=(X,P)} \newcommand{\QYQ}{\mathbf{Q}=(Y,Q)} \newcommand{\GVE}{\mathbf{G}=(V,E)} \newcommand{\HWF}{\mathbf{H}=(W,F)} \newcommand{\bfC}{\mathbf{C}} \newcommand{\bfG}{\mathbf{G}} \newcommand{\bfH}{\mathbf{H}} \newcommand{\bfF}{\mathbf{F}} \newcommand{\bfI}{\mathbf{I}} \newcommand{\bfK}{\mathbf{K}} \newcommand{\bfP}{\mathbf{P}} \newcommand{\bfQ}{\mathbf{Q}} \newcommand{\bfR}{\mathbf{R}} \newcommand{\bfS}{\mathbf{S}} \newcommand{\bfT}{\mathbf{T}} \newcommand{\bfNP}{\mathbf{NP}} \newcommand{\bftwo}{\mathbf{2}} \newcommand{\cgA}{\mathcal{A}} \newcommand{\cgB}{\mathcal{B}} \newcommand{\cgC}{\mathcal{C}} \newcommand{\cgD}{\mathcal{D}} \newcommand{\cgE}{\mathcal{E}} \newcommand{\cgF}{\mathcal{F}} \newcommand{\cgG}{\mathcal{G}} \newcommand{\cgM}{\mathcal{M}} \newcommand{\cgN}{\mathcal{N}} \newcommand{\cgP}{\mathcal{P}} \newcommand{\cgR}{\mathcal{R}} \newcommand{\cgS}{\mathcal{S}} \newcommand{\bfn}{\mathbf{n}} \newcommand{\bfm}{\mathbf{m}} \newcommand{\bfk}{\mathbf{k}} \newcommand{\bfs}{\mathbf{s}} \newcommand{\bijection}{\xrightarrow[\text{onto}]{\text{$1$--$1$}}} \newcommand{\injection}{\xrightarrow[]{\text{$1$--$1$}}} \newcommand{\surjection}{\xrightarrow[\text{onto}]{}} \newcommand{\nin}{\not\in} \newcommand{\prufer}{\mbox{prüfer}} \DeclareMathOperator{\fix}{fix} \DeclareMathOperator{\stab}{stab} \DeclareMathOperator{\var}{var} \newcommand{\inv}{^{-1}} \newcommand{\lt}{ < } \newcommand{\gt}{ > } \newcommand{\amp}{ & } \)


A unique feature of this book is a recurring cast of characters: Alice, Bob, Carlos, Dave, Xing, Yolanda and Zori. They are undergraduate students at Georgia Tech, they're taking an 8:05am section of Math 3012: Applied Combinatorics, and they frequently go for coffee at the Clough Undergraduate Learning Center immediately after the class is over. They've become friends of sorts and you may find their conversations about Applied Combinatorics of interest, as they will may reveal subtleties behind topics currently being studied, reinforce connections with previously studied material or set the table for topics which will come later. Sometimes, these conversations will set aside in a clearly marked Discussion section, but they will also be sprinkled as brief remarks throughout the text.

In time, you will get to know these characters and will sense that, for example, when Dave comments on a topic, it will represent a perspective that Zori is unlikely to share. Some comments are right on target while others are “out in left field.” Some may even be humorous, at least we hope this is the case. Regardless, our goal is not to entertain—although that is not all that bad a side benefit. Instead, we intend that our informal approach adds to the instructional value of our text.

Now it is time to meet our characters:

Alice is a computer engineering major from Philadelphia. She is ambitious, smart and intense. Alice is quick to come to conclusions, most of which are right. On occasion, Alice is not kind to Bob.

Bob is a management major from Omaha. He is a hard working and conscientious. Bob doesn't always keep pace with his friends, but anything he understands, he owns, and in the end, he gets almost everything. On the other hand, Bob has never quite understood why Alice is short with him at times.

Carlos is a really, really smart physics major from San Antonio. He has three older brothers and two sisters, one older, one younger. His high school background wasn't all that great, but Carlos is clearly a special student at Georgia Tech. He absorbs new concepts at lightning speed and sees through to the heart of almost every topic. He thinks carefully before he says something and is admirably polite.

Dave is a discrete math major from Los Angeles. Dave is a flake. He's plenty smart enough but not all that diligent. Still, he has unique insights into things and from time to time says something worth hearing—not always but sometimes. His friends say that Dave suffers from occasional brain–mouth disconnects.

Xing is a computer science major from New York. Xing's parents immigrated from Beijing, and he was strongly supported and encouraged in his high school studies. Xing is detail oriented and not afraid to work hard.

Yolanda is a double major (computer science and chemistry) from Cumming, a small town just north of Atlanta. Yolanda is the first in her extended family to go to a college or university. She is smart and absorbs knowledge like a sponge. It's all new to her and her horizons are raised day by day.

Zori is an applied math major from Detroit. She is bottom-line focused, has little time for puzzles and always wants to see applications to justify why something is included in the course. Zori is determined, driven and impatient at times.