GL(n, q)-analogues of factorization problems in the symmetric group
We consider GLn (Fq)-analogues of certain factorization problems in the symmetric group Sn: ratherthan counting factorizations of the long cycle(1,2, . . . , n) given the number of cycles of each factor, we countfactorizations of a regular elliptic element given the fixed space dimension of each fac...
Saved in:
| Published in: | Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings, 28th... |
|---|---|
| Main Authors: | , |
| Format: | Journal Article Conference Proceeding |
| Language: | English |
| Published: |
DMTCS
22.04.2020
Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| ISSN: | 1365-8050, 1462-7264, 1365-8050 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We consider GLn (Fq)-analogues of certain factorization problems in the symmetric group Sn: ratherthan counting factorizations of the long cycle(1,2, . . . , n) given the number of cycles of each factor, we countfactorizations of a regular elliptic element given the fixed space dimension of each factor. We show that, as in Sn, the generating function counting these factorizations has attractive coefficients after an appropriate change of basis.Our work generalizes several recent results on factorizations in GLn (Fq) and also uses a character-based approach.We end with an asymptotic application and some questions. |
|---|---|
| ISSN: | 1365-8050 1462-7264 1365-8050 |
| DOI: | 10.46298/dmtcs.6382 |