Lewis, Joel Brewster and Morales, Alejandro H. - GL(n, q)-analogues of factorization problems in the symmetric group

dmtcs:6382 - Discrete Mathematics & Theoretical Computer Science, April 22, 2020, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
GL(n, q)-analogues of factorization problems in the symmetric group

Authors: Lewis, Joel Brewster and Morales, Alejandro H.

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.


Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Published on: April 22, 2020
Submitted on: July 4, 2016
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]


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