  We define some generalizations of the classical descent and inversion
statistics on signed permutations that arise from the work of Sack and
Ulfarsson [20] and called after width-k descents and width-k inversionsof type
A in Davis's work [8]. Using the aforementioned new statistics, we derive some
new generalizations of Eulerian polynomials of type A, B and D. It should also
be noticed that we establish the Gamma-positivity of the "width-k" Eulerian
polynomials and we give a combinatorial interpretation of finite sequences
associated to these new polynomials using quasisymmetric functions and
P-partition in Petersen's work [18].
