In the DPV algorithm book I see an array split like so:
$x_L, x_R$ = leftmost $\lceil n/2 \rceil $, rightmost $\lfloor n/2 \rfloor$
This is not something I have seen before as in the odd case you have 1 to k, k+1 to n but in the even case you have 1 to k, k to n.