Representations in Table 3
\(a\) |
\(b\) |
\(N\) |
\(P_v\) |
|---|---|---|---|
1 |
3 |
1 |
\(3s_{1, 1, 1} +s_{1} + s_{1, 1}\) |
1 |
6 |
2 |
\(s_{1} + s_{1, 1} + s_{2} + 3s_{2, 1} + s_{2, 2} + s_{3, 1} + s_{3, 2}\) |
1 |
9 |
3 |
\(s_{3, 1} + s_{3, 2} + s_{4, 1} + 3s_{4, 2} + s_{4, 3} + s_{5, 2} + s_{5, 3}\) |
1 |
12 |
4 |
\(s_{5, 2} + s_{5, 3} + s_{6, 2} + 3s_{6, 3} + s_{6, 4} + s_{7, 3} + s_{7, 4}\) |
1 |
15 |
5 |
\(s_{7, 3} + s_{7, 4} + s_{8, 3} + 3s_{8, 4} + s_{8, 5} + s_{9, 4} + s_{9, 5}\) |
2 |
3 |
1 |
\(11s_{1 , 1, 1} + 7s_{1} + 7s_{1, 1} + s_{2} + 2s_{2, 1} + s_{2, 2}\) |
2 |
6 |
1 |
\(3s_{1, 1, 1} + 3s_{1} + 3s_{1, 1} + 9s_{2} + 7s_{2, 1} + 9s_{2, 2} + 6s_{3} + 9s_{3, 1} + 9s_{3, 2} + 6s_{3, 3} + s_{4} + 3s_{4, 1} + 7s_{4, 2} + 3s_{4, 3} + s_{4, 4} + s_{5} + 3s_{5, 2} + 3s_{5, 3} + s_{5, 5} + s_{6, 3}\) |
2 |
9 |
1 |
\(3s_{1, 1, 1} + 12s_{3, 1} + 12s_{3, 2} + 9s_{4, 1} + 15s_{4, 2} + 9s_{4, 3} + 4s_{5, 1} + 6s_{5, 2} + 6s_{5, 3} + 4s_{5, 4} + 3s_{6, 1} + 3s_{6, 2} + 4s_{6, 3} + 3s_{6, 4} + 3s_{6, 5} + s_{7} + 3s_{7, 1} + 5s_{7, 2} + 3s_{7, 3} + 3s_{7, 4} + 5s_{7, 5} + 3s_{7, 6} + s_{7, 7} + s_{8} + 3s_{8, 2} + 3s_{8, 3} + s_{8, 4} + 3s_{8, 5} + 3s_{8, 6} + s_{8, 8} + s_{9, 3} + s_{9, 6}\) |
2 |
12 |
1 |
\(4s_{4} + 9s_{4, 2} + 4s_{4, 4} + s_{5, 2} + s_{5, 3} + 3s_{6, 1} + 4s_{6, 2} + 3s_{6, 3} + 4s_{6, 4} + 3s_{6, 5} + 4s_{7} + 9s_{7, 1} + 8s_{7, 2} + 12s_{7, 3} + 12s_{7, 4} + 8s_{7, 5} + 9s_{7, 6} + 4s_{7, 7} + 4s_{8, 1} + 2s_{8, 2} + 4s_{8, 3} + 10s_{8, 4} + 4s_{8, 5} + 2s_{8, 6} + 4s_{8, 7} + s_{9, 1} + s_{9, 3} + 5s_{9, 4} + 5s_{9, 5} + s_{9, 6} + s_{9, 8} + s_{10, 3} + 4s_{10, 4} + 4s_{10, 6} + s_{10, 7} + s_{11} + 4s_{11, 4} + s_{11, 5} + s_{11, 6} + 4s_{11, 7} + s_{11, 11} + s_{12, 3} + 2s_{12, 4} + 3s_{12, 5} + s_{12, 6} + 3s_{12, 7} + 2s_{12, 8} + s_{12, 9}\) |
2 |
15 |
1 |
\(2s_{1, 1, 1} + 14s_{1} + 5s_{1, 1} + 11s_{2} + s_{2, 1} + s_{2, 2} + s_{3, 1} + s_{3, 3} + s_{4} + 2s_{4, 2} + 6s_{4, 4} + 2s_{5} + 2s_{5, 4} + 3s_{5, 5} + s_{6} + 4s_{6, 1} + 2s_{6, 2} + 2s_{6, 3} + 9s_{6, 4} + s_{6, 5} + 3s_{7} + 3s_{7, 1} + 3s_{7, 3} + s_{7, 4} + 5s_{7, 5} + s_{7, 7} + 2s_{8} + 4s_{8, 1} + 6s_{8, 2} + s_{8, 3} + 3s_{8, 4} + 4s_{8, 5} + 2s_{8, 6} + 2s_{8, 7} + s_{8, 8} + s_{9} + s_{9, 1} + 12s_{9, 2} + 6s_{9, 3} + 2s_{9, 4} + 3s_{9, 5} + 9s_{9, 6} + 8s_{9, 7} + 6s_{9, 8} + 4s_{10, 2} + 5s_{10, 3} + 8s_{10, 4} + 3s_{10, 5} + 7s_{10, 6} + 9s_{10, 7} + 2s_{10, 8} + s_{11} + s_{11, 1} + 4s_{11, 2} + 5s_{11, 4} + 3s_{11, 6} + s_{11, 7} + s_{11, 8} + s_{11, 9} + 2s_{11, 10} + s_{11, 11} + s_{12, 2} + s_{12, 3} + 3s_{12, 6} + 5s_{12, 9} + s_{12, 11} + s_{13} + s_{13, 1} + 4s_{13, 5} + 6s_{13, 6} + 6s_{13, 7} + s_{13, 8} + 2s_{13, 9} + s_{13, 12} + s_{14} + 3s_{14, 2} + 2s_{14, 3} + 2s_{14, 5} + 2s_{14, 6} + 3s_{14, 7} + s_{14, 8} + 4s_{14, 11} + s_{14, 14} + s_{15, 3} + 3s_{15, 7} + 3s_{15, 8} + 2s_{15, 11} + s_{15, 12} + s_{16, 7} + 3s_{16, 8}\) |
3 |
3 |
1 |
\(47s_{1, 1, 1} + 42s_{1} + 42s_{1, 1} + 12s_{2} + 22s_{2, 1} + 12s_{2, 2} + s_{3} + 3s_{3, 1} + 3s_{3, 2} + s_{3, 3}\) |
3 |
6 |
2 |
\(112s_{2} + 2s_{2, 1} + 112s_{2, 2} + 279s_{3} + 323s_{3, 1} + 323s_{3, 2} + 279s_{3, 3} + 100s_{4} + 269s_{4, 1} + 402s_{4, 2} + 269s_{4, 3} + 100s_{4, 4} + 27s_{5, 1} + 195s_{5, 2} + 195s_{5, 3} + 27s_{5, 4} + 5s_{6, 1} + 67s_{6, 2} + 133s_{6, 3} + 67s_{6, 4} + 5s_{6, 5} + s_{7} + 16s_{7, 2} + 41s_{7, 3} + 41s_{7, 4} + 16s_{7, 5} + s_{7, 7} + s_{8, 1} + 2s_{8, 2} + 9s_{8, 3} + 12s_{8, 4} + 9s_{8, 5} + 2s_{8, 6} + s_{8, 7} + s_{9, 4} + s_{9, 5}\) |
3 |
9 |
1 |
\(3s_{3 , 1} + 3s_{3, 2} + 24s_{4} + 5s_{4, 2} + 24s_{4, 4} + 198s_{5} + 216s_{5, 1} + 42s_{5, 2} + 42s_{5, 3} + 216s_{5, 4} + 198s_{5, 5} + 135s_{6} + 409s_{6, 1} + 418s_{6, 2} + 149s_{6, 3} + 418s_{6, 4} + 409s_{6, 5} + 135s_{6, 6} + 100s_{7, 1} + 335s_{7, 2} + 278s_{7, 3} + 278s_{7, 4} + 335s_{7, 5} + 100s_{7, 6} + 11s_{8, 2} + 118s_{8, 3} + 224s_{8, 4} + 118s_{8, 5} + 11s_{8, 6} + 4s_{9, 2} + 7s_{9, 3} + 208s_{9, 4} + 208s_{9, 5} + 7s_{9, 6} + 4s_{9, 7} + 61s_{10, 4} + 178s_{10, 5} + 61s_{10, 6} + s_{11, 3} + 4s_{11, 4} + 67s_{11, 5} + 67s_{11, 6} + 4s_{11, 7} + s_{11, 8} + s_{12} + 2s_{12, 4} + 18s_{12, 5} + 46s_{12, 6} + 18s_{12, 7} + 2s_{12, 8} + s_{12, 12} + s_{13, 5} + 11s_{13, 6} + 11s_{13, 7} + s_{13, 8} + s_{14, 5} + 3s_{14, 6} + 6s_{14, 7} + 3s_{14, 8} + s_{14, 9}\) |
3 |
12 |
2 |
\(s_{5} + 2s_{6, 1} + 3s_{6, 2} + s_{6, 3} + 2s_{6, 5} + 429s_{7} + 357s_{7, 1} + 4s_{7, 2} + 8s_{7, 3} + 6s_{7, 4} + 4s_{7, 5} + 363s_{7, 6} + 429s_{7, 7} + 502s_{8} + 1176s_{8, 1} + 1061s_{8, 2} + 421s_{8, 3} + 27s_{8, 4} + 463s_{8, 5} + 1061s_{8, 6} + 1176s_{8, 7} + 499s_{8, 8} + 53s_{9} + 521s_{9, 1} + 1381s_{9, 2} + 1770s_{9, 3} + 695s_{9, 4} + 725s_{9, 5} + 1770s_{9, 6} + 1346s_{9, 7} + 521s_{9, 8} + 53s_{9, 9} + 199s_{10, 2} + 974s_{10, 3} + 990s_{10, 4} + 37s_{10, 5} + 978s_{10, 6} + 974s_{10, 7} + 199s_{10, 8} + 2s_{10, 9} + 5s_{11, 1} + s_{11, 2} + 2s_{11, 3} + 474s_{11, 4} + 417s_{11, 5} + 393s_{11, 6} + 474s_{11, 7} + 28s_{11, 8} + s_{11, 9} + 5s_{11, 10} + s_{12, 2} + s_{12, 4} + 471s_{12, 5} + 938s_{12, 6} + 453s_{12, 7} + s_{12, 8} + s_{12, 10} + s_{13, 5} + 659s_{13, 6} + 659s_{13, 7} + s_{13, 8} + 221s_{14, 6} + 658s_{14, 7} + 221s_{14, 8} + 281s_{15, 7} + 281s_{15, 8} + s_{16} + 2s_{16, 4} + 83s_{16, 7} + 252s_{16, 8} + 83s_{16, 9} + 2s_{16, 12} + s_{16, 16} + s_{17, 1} + s_{17, 5} + s_{17, 6} + 92s_{17, 8} + 92s_{17, 9} + s_{17, 11} + s_{17, 12} + s_{17, 16} + 2s_{18, 7} + 24s_{18, 8} + 69s_{18, 9} + 24s_{18, 10} + 2s_{18, 11} + s_{19, 8} + 17s_{19, 9} + 17s_{19, 10} + s_{19, 11} + 3s_{20, 9} + 9s_{20, 10} + 3s_{20, 11} + s_{21, 10} + s_{21, 11}\) |