  A $k$-uniform hypergraph $H = (V, E)$ is $k$-partite if $V$ can be
partitioned into $k$ sets $V_1, \ldots, V_k$ such that every edge in $E$
contains precisely one vertex from each $V_i$. We call such a graph
$n$-balanced if $|V_i| = n$ for each $i$. An independent set $I$ in $H$ is
balanced if $|I\cap V_i| = |I\cap V_j|$ for each $1 \leq i, j \leq k$, and a
coloring is balanced if each color class induces a balanced independent set in
$H$. In this paper, we provide a lower bound on the balanced independence
number $\alpha_b(H)$ in terms of the average degree $D = |E|/n$, and an upper
bound on the balanced chromatic number $\chi_b(H)$ in terms of the maximum
degree $\Delta$. Our results recover those of recent work of Chakraborti for $k
= 2$.
