| Autor: |
Joel Brewster Lewis, Ricky Ini Liu, Alejandro H. Morales, Greta Panova, Steven V Sam, Yan Zhang |
| Jazyk: |
angličtina |
| Rok vydání: |
2011 |
| Předmět: |
|
| Zdroj: |
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AO,..., Iss Proceedings (2011) |
| Druh dokumentu: |
article |
| ISSN: |
1365-8050 |
| DOI: |
10.46298/dmtcs.2941 |
| Popis: |
We study the functions that count matrices of given rank over a finite field with specified positions equal to zero. We show that these matrices are $q$-analogues of permutations with certain restricted values. We obtain a simple closed formula for the number of invertible matrices with zero diagonal, a $q$-analogue of derangements, and a curious relationship between invertible skew-symmetric matrices and invertible symmetric matrices with zero diagonal. In addition, we provide recursions to enumerate matrices and symmetric matrices with zero diagonal by rank. Finally, we provide a brief exposition of polynomiality results for enumeration questions related to those mentioned, and give several open questions. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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