Name
Abstract | ||
|---|---|---|
A biplane is a 2-(k(k-1)/2 + 1, k, 2) symmetric design. Only six-teen nontrivial biplanes are known: there are exactly nine biplanes with k < 11, at least five biplanes with k = 11, and at least two bi-planes with k = 13.It is here shown by exhaustive computer search that the list of five known biplanes with k = 11 is complete. This result further implies that there exists no 3-(57, 12, 2) design, no 112<SUB>11 sym-metric configuration, and no (324, 57, 0, 12) strongly regular graph. The five biplanes have 16 residual designs, which by the Hall-Connor theorem constitute a complete classification of the 2-(45, 9, 2) designs. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1016/j.endm.2006.08.063 | Electronic Notes in Discrete Mathematics |
Keywords | Field | DocType |
biplane,classification,strongly regular graph,symmetric configuration,symmetric design | Discrete mathematics,Combinatorics,Strongly regular graph,Biplane,Symmetric design,Mathematics | Journal |
Volume | ISSN | Citations |
27 | 1571-0653 | 4 |
PageRank | References | Authors |
0.53 | 6 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Patric R. J. Östergård | 1 | 609 | 70.61 |
| Petteri Kaski | 2 | 912 | 66.03 |