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 |
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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 |
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Leech’s lattice, p. 200 |
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