  SLOPE is a popular method for dimensionality reduction in the
high-dimensional regression. Indeed some regression coefficient estimates of
SLOPE can be null (sparsity) or can be equal in absolute value (clustering).
Consequently, SLOPE may eliminate irrelevant predictors and may identify groups
of predictors having the same influence on the vector of responses. The notion
of SLOPE pattern allows to derive theoretical properties on sparsity and
clustering by SLOPE. Specifically, the SLOPE pattern of a vector provides: the
sign of its components (positive, negative or null), the clusters (indices of
components equal in absolute value) and clusters ranking. In this article we
give a necessary and sufficient condition for SLOPE pattern recovery of an
unknown vector of regression coefficients.
