Abstract
We investigate symmetric (0, 1) matrices on which the permanent is convertible to the determinant by assigning ± signs to their entries. In particular, we obtain several quantitative bounds for the number of nonzero elements of such matrices, including the analog of Gibson's theorem for symmetric matrices.
| Original language | English |
|---|---|
| Pages (from-to) | 624-635 |
| Number of pages | 12 |
| Journal | Mathematical Notes |
| Volume | 92 |
| Issue number | 5-6 |
| DOIs | |
| State | Published - 2012 |
| Externally published | Yes |
Bibliographical note
Funding Information:The work is supported in part by the joint Slovenian–Russian grant no. BI-RU/12-13-022. The work of the first author is also partially supported by grant no. MD-2502.2012.1 and by the Russian Foundation for Basic Research (grant no. 12-01-00140-a).
Funding
The work is supported in part by the joint Slovenian–Russian grant no. BI-RU/12-13-022. The work of the first author is also partially supported by grant no. MD-2502.2012.1 and by the Russian Foundation for Basic Research (grant no. 12-01-00140-a).
| Funders | Funder number |
|---|---|
| Russian Foundation for Basic Research | 12-01-00140-a |
Keywords
- conversion
- determinant
- permanent
- symmetric matrix