Summary: We introduce new natural generalizations of the classical descent and inversion statistics for permutations, called $width-k$ descents and $width-k$ inversions. These variations induce generalizations of the excedance and major statistics, providing a framework in which well-known equidistributivity results for classical statistics are paralleled. We explore additional relationships among the statistics providing specific formulas in certain special cases. Moreover, we explore the behavior of these width-$k$ statistics in the context of pattern avoidance.

05A05, 05A15

permutation statistics, pattern avoidance, generating function