An -descent in a permutation is a pair of adjacent elements
such that the first element is from , the second element is from
, and the first element is greater than the second one. An
-adjacency in a permutation is a pair of adjacent elements
such that the first one is from and the second one is from .
An -place-value pair in a permutation is an element in
position , such that is in and is in . It turns
out, that for certain choices of and some of the three
statistics above become equidistributed. Moreover, it is easy to
derive the distribution formula for -place-value pairs thus
providing distribution for other statistics under consideration too.
This generalizes some results in the literature. As a result of our
considerations, we get combinatorial proofs of several remarkable
identities. We also conjecture existence of a bijection between two
objects in question preserving a certain statistic.