Name
Abstract | ||
|---|---|---|
We say that a diagonal in an array is λ-balanced if each entry occurs λ times. Let L be a frequency square of type F(n;λ); that is, an n×n array in which each entry from {1,2,…,m=n∕λ} occurs λ times per row and λ times per column. We show that if m⩽3, L contains a λ-balanced diagonal, with only one exception up to equivalence when m=2. We give partial results for m⩾4
and suggest a generalization of Ryser’s conjecture, that every Latin square of odd order has a transversal. Our method relies on first identifying a small substructure with the frequency square that facilitates the task of locating a balanced diagonal in the entire array. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.disc.2018.04.029 | Discrete Mathematics |
Keywords | Field | DocType |
05B15,05C15 | Diagonal,Discrete mathematics,Combinatorics,Latin square,Transversal (geometry),Equivalence (measure theory),Conjecture,Mathematics,Substructure | Journal |
Volume | Issue | ISSN |
341 | 8 | 0012-365X |
Citations | PageRank | References |
0 | 0.34 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Nicholas J. Cavenagh | 1 | 92 | 20.89 |
| Adam Mammoliti | 2 | 0 | 1.35 |