Name
Abstract | ||
|---|---|---|
We present several fundamental duality theorems for matroids and more general combinatorial structures. As a special case, these results show that the maximal cardinalities of fixed-ranked sets of a matroid determine the corresponding maximal cardinalities of the dual matroid. Our main results are applied to perfect matroid designs, graphs, transversals, and linear codes over division rings, in each case yielding a duality theorem for the respective class of objects. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/s10623-011-9524-y | Des. Codes Cryptography |
Keywords | Field | DocType |
Matroid duality theorems,Demi-matroid,Poset code,Wei’s Duality Theorem,Matroid design,05B35,06A07,94B05 | Matroid,Discrete mathematics,Combinatorics,Duality (mathematics),Oriented matroid,Dual matroid,Matroid partitioning,Duality (optimization),Graphic matroid,Weighted matroid,Mathematics | Journal |
Volume | Issue | ISSN |
62 | 3 | 0925-1022 |
Citations | PageRank | References |
10 | 0.77 | 9 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Thomas Britz | 1 | 88 | 8.89 |
| Trygve Johnsen | 2 | 33 | 7.94 |
| Dillon Mayhew | 3 | 102 | 18.63 |
| Keisuke Shiromoto | 4 | 39 | 8.41 |