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Appendix C List 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 |
