Sách MacMahon’s theorem for a set of permutations with given descent indices and right-maximal records

There exist other kinds of permutation records. These depend on three parameters:
direction (right-to-left or left-to-right), extremum (maximum or minimum) and place
(index or value). Write down a permutation record briefly as f[g, h], where f = r, l; g =
max, min; and h = i, v. Here “r,l” corresponds to “right-to-left, left-to-right”; “max,min”
to “maximum, minimum”; and “i,v” to “index, value”.
Example. If σ = 516423, then