APPENDIX B
NOTATION
n! | n factorial, p. 4 |
N | {1, 2, 3,…}, p. 6 |
Nm | {1, 2, 3,…,m}, p. 6 |
binomial coefficient, p. 8 | |
multinomial coefficient, p. 9 | |
B(n) | Bell number, p. 22 |
p(n) | partition number, p. 22 |
p(n, k) | partition number, p. 22 |
dn | derangement number, p. 24 |
Fn | Fibonacci number, p. 31 |
Ln | Lucas number, p. 37 |
Stirling number of the second kind, p. 40 | |
Stirling number of the first kind, p. 41 | |
db(n) | digital sum, p. 46 |
Cn | Catalan number, p. 64 |
tn | number of transitive and reflexive relations, p. 69 |
pn | number of partial orders, p. 69 |
Zn | cyclic group, p. 86 |
Sn | symmetric group, p. 87 |
Dn | dihedral group, p. 88 |
An | alternating group, p. 88 |
g(n) | number of nonisomorphic graphs, p. 101 |
n(k, d) | lattice point function, p. 112 |
n′(k, d) | generalized SET® function, p. 112 |
δ(g) | degree of vertex, p. 115 |
complement graph, p. 115 | |
Kn | complete graph, p. 115 |
Km,n | complete bipartite graph, p. 115 |
K∞ | infinite complete graph, p. 115 |
K∞,∞ | infinite complete bipartite graph, p. 115 |
Cn | cycle, p. 115 |
Pn | path, p. 115 |
α(G) | independence number, p. 116 |
χ(G) | chromatic number, p. 116 |
R(m, n) | Ramsey number, p. 133 |
R(a1,…,ac) | multiple color Ramsey number, p. 135 |
R(a1,…,ac; t) | hypergraph Ramsey number, p. 136 |
[S]t | complete t-uniform hypergraph, 136 |
S(c) | Schur number, p. 145 |
W(c, l) | van der Waerden number, p. 148 |
FC | Fano Configuration, p. 162 |
GL(n, q) | general linear group, p. 164 |
SL(n, q) | special linear group, p. 164 |
PGL(n, q) | projective general linear group, p. 165 |
PSL(n, q) | projective special linear group, p. 165 |
t-(v, k, λ) | t-design, p. 171 |
S(t, k, v) | Steiner system, p. 173 |
(v, b, r, k, λ) BIBD | balanced incomplete block design, p. 175 |
(v, k, λ) SBD | square block design, p. 177 |
πn | projective plane, p. 180 |
π’n | affine plane, p. 182 |
L | Latin square, p. 183 |
MOLS | mutually orthogonal Latin squares, p. 185 |
OOD | ordered orthogonal design, p. 188 |
G23 | Golay code, p. 194 |
G24 | extended Golay code, p. 194 |
Leech’s lattice, p. 200 |
18.191.195.183