  We investigate the relations between different variants of the LZ77 parsing
existing in the literature. All of them are defined as greedily constructed
parsings encoding each phrase by reference to a string occurring earlier in the
input. They differ by the phrase encodings: encoded by pairs (length + position
of an earlier occurrence) or by triples (length + position of an earlier
occurrence + the letter following the earlier occurring part); and they differ
by allowing or not allowing overlaps between the phrase and its earlier
occurrence. For a given string of length $n$ over an alphabet of size $\sigma$,
denote the numbers of phrases in the parsings allowing (resp., not allowing)
overlaps by $z$ (resp., $\hat{z}$) for "pairs", and by $z_3$ (resp.,
$\hat{z}_3$) for "triples". We prove the following bounds and provide series of
examples showing that these bounds are tight:
  $\bullet$ $z \le \hat{z} \le z \cdot O(\log\frac{n}{z\log_\sigma z})$ and
$z_3 \le \hat{z}_3 \le z_3 \cdot O(\log\frac{n}{z_3\log_\sigma z_3})$;
  $\bullet$ $\frac{1}2\hat{z} < \hat{z}_3 \le \hat{z}$ and $\frac{1}2 z < z_3
\le z$.
