  A $k$-plex of a latin square is a collection of cells representing each row,
column, and symbol precisely $k$ times. The classic case of $k=1$ is more
commonly known as a transversal. We introduce the concept of a $k$-weight, an
integral weight function on the cells of a latin square whose row, column, and
symbol sums are all $k$. We then show that several non-existence results about
$k$-plexes can been seen as more general facts about $k$-weights and that the
weight-analogues of several well-known existence conjectures for plexes
actually hold for $k$-weights.
