## AppendixCList of Notation

Symbol Description Location
$n!$ $n$ factorial Paragraph
$P(m,n)$ number of permutations Paragraph
$\binom{n}{k}$ binomial coefficient Paragraph
$C(n,k)$ binomial coefficient (inline) Paragraph
$\binom{n}{k_1,k_2,k_3,\dots,k_r}$ multinomial coefficient Paragraph
$\cgP$ polynomial time problems Paragraph
$\cgN\cgP$ nondeterministic polynomial time problems Paragraph
$\deg_\bfG(v)$ degree of vertex $v$ in graph $\bfG$ Paragraph
$\bfK_n$ complete graph on $n$ vertices Paragraph
$\bfI_n$ independent graph on $n$ vertices Paragraph
$\bfP_n$ path with $n$ vertices Paragraph
$\bfC_n$ path with $n$ vertices Paragraph
$\chi(\bfG)$ chromatic number of a graph $\bfG$ Paragraph
$\omega(\bfG)$ clique number of $\bfG$ Paragraph
$x\| y$ $x$ and $y$ are incomparable Paragraph
$\height(\bfP)$ height of poset $\bfP$ Paragraph
$\width(\bfP)$ width of poset $\bfP$ Paragraph
$D(x), D(S),D[x], D[S]$ down set Paragraph
$U(x), U(S), U[x], U[S]$ up set Paragraph
$\bfn$ chain with $n$ points Paragraph
$\bfP+\bfQ$ disjoint sum of posets Paragraph
$\phi(n)$ Euler $\phi$ function Paragraph
$\binom{p}{k}$ generalized binomial coefficient Definition 8.9
$Af(n)$ advancement operator applied to $f(n)$ Paragraph
$P(A|B)$ probability of $A$ given $B$ Paragraph
$C(X,k)$ family of all $k$-element subsets of $X$ Paragraph
$R(m,n)$ Ramsey number Paragraph
$\langle C\rangle$ equivalence class of $C$ Paragraph
$\stab_G(C)$ stabilizer of $C$ under action of $G$ Paragraph
$\overline{E}$ complement of event $E$ Paragraph
$x\in X$ $x$ is a member of the set $X$ Paragraph
$x\notin X$ $x$ is not a member of the set $X$ Paragraph
$X\cap Y$ intersection of $X$ and $Y$ Paragraph
$X\cup Y$ union of $X$ and $Y$ Paragraph
$\emptyset$ empty set Paragraph
$\posints$ set of positive integers Paragraph
$\ints$ set of integers Paragraph
$\rats$ set of rational numbers Paragraph
$\reals$ set of real numbers Paragraph
$\nonnegints$ set of non-negative integers Paragraph
$[n]$ $\{1,2,\dots,n\}$ Paragraph
$X\subseteq Y$ $X$ is a subset of $Y$ Paragraph
$X\subsetneq Y$ $X$ is a proper subset of $Y$ Paragraph
$X\times Y$ cartesian product of $X$ and $Y$ Paragraph
$f\colon X\rightarrow Y$ $f$ is a function from $X$ to $Y$ Paragraph
$f:X\injection Y$ $f$ is an injection from $X$ to $Y$ Paragraph
$f\colon X\surjection Y$ $f$ is a surjection from $X$ to $Y$ Paragraph
$f\colon X\bijection Y$ $f$ is a bijection from $X$ to $Y$ Paragraph
$|X|$ cardinality of set $X$ Paragraph