3 research outputs found
On the determinants and permanents of matrices with restricted entries over prime fields
Let be a set in a prime field . In this paper, we prove
that matrices with entries in determine almost
distinct determinants and almost
distinct permanents when is small enough.Comment: Submitted for publicatio
On growth of the number of determinants with restricted entries
Let be a finite subset of a field and be a set of
all matrices with entries in , namely where
the symbol defines the matrix with elements . How big is the
size of the set comparing to the size of the set
Expanding phenomena over higher dimensional matrix rings
In this paper, we study the expanding phenomena in the setting of higher
dimensional matrix rings. More precisely, we obtain a sum-product estimate for
large subsets and show that x+yz, x(y+z) are moderate expanders over the matrix
ring, and xy + z + t is strong expander over the matrix rings. These results
generalize recent results of Y.D. Karabulut, D. Koh, T. Pham, C-Y. Shen, and
the second listed author.Comment: Available Online in Journal of Number Theory, 21 page