MMN-1075
Natural density of relative coprime polynomials in $\mathbb{F}_q[x]$
Xiangqian Guo; Fengdan Hou; Xuewen Liu;Abstract
Let $\F_q[x]$ be the polynomial ring over the finite field $\F_q$ containing $q$ elements. We compute the natural density of rank-$n$ vectors over $\F_q[x]$ whose entries are $k$-wise relatively coprime, which can be interpreted as the probability that $n$ polynomials in $\F_q[x]$ are $k$-wise relatively coprime. As a special case, we get the probability that $n$ polynomials in $\F_q[x]$ are pairwise coprime.
Vol. 15 (2014), No. 2, pp. 481-488