  Let $S_n$ denote the symmetric group. For any $\sigma \in S_n$, we let
$\mathrm{des}(\sigma)$ denote the number of descents of $\sigma$,
$\mathrm{inv}(\sigma)$ denote the number of inversions of $\sigma$, and
$\mathrm{LRmin}(\sigma)$ denote the number of left-to-right minima of $\sigma$.
For any sequence of statistics $\mathrm{stat}_1, \ldots \mathrm{stat}_k$ on
permutations, we say two permutations $\alpha$ and $\beta$ in $S_j$ are
$(\mathrm{stat}_1, \ldots \mathrm{stat}_k)$-c-Wilf equivalent if the generating
function of $\prod_{i=1}^k x_i^{\mathrm{stat}_i}$ over all permutations which
have no consecutive occurrences of $\alpha$ equals the generating function of
$\prod_{i=1}^k x_i^{\mathrm{stat}_i}$ over all permutations which have no
consecutive occurrences of $\beta$. We give many examples of pairs of
permutations $\alpha$ and $\beta$ in $S_j$ which are $\mathrm{des}$-c-Wilf
equivalent, $(\mathrm{des},\mathrm{inv})$-c-Wilf equivalent, and
$(\mathrm{des},\mathrm{inv},\mathrm{LRmin})$-c-Wilf equivalent. For example, we
will show that if $\alpha$ and $\beta$ are minimally overlapping permutations
in $S_j$ which start with 1 and end with the same element and
$\mathrm{des}(\alpha) = \mathrm{des}(\beta)$ and $\mathrm{inv}(\alpha) =
\mathrm{inv}(\beta)$, then $\alpha$ and $\beta$ are
$(\mathrm{des},\mathrm{inv})$-c-Wilf equivalent.
