20 citations · 38 across the 9 of their papers we have counts for
12 papers · 1 filter
Equi-distribution over Descent Classes of the Hyperoctahedral Group
R. M. Adin, F. Brenti, Y. Roichman
A classical result of MacMahon shows that the length function and the major index are equi-distributed over the symmetric group. Foata and Schützenberger gave a remarkable refineme…
On Degrees in the Hasse Diagram of the Strong Bruhat Order
Ron M. Adin, Yuval Roichman
For a permutation in the symmetric group let the {\it total degree} be its valency in the Hasse diagram of the strong Bruhat order on , and let the {\it down degree}…
Statistics on Wreath Products and Generalized Binomial-Stirling Numbers
Amitai Regev, Yuval Roichman
Various statistics on wreath products are defined via canonical words, "colored" right to left minima and "colored" descents. It is shown that refined counts with respect to these…
Signed Mahonians
Ron M. Adin, Ira M. Gessel, Yuval Roichman
A classical result of MacMahon gives a simple product formula for the generating function of major index over the symmetric group. A similar factorial-type product formula for the…
q Statistics on and Pattern Avoidance
Amitai Regev, Yuval Roichman
Natural q analogues of classical statistics on the symmetric groups are introduced; parameters like: the q-length, the q-inversion number, the q-descent number and the q-majo…
Equidistribution and Sign-Balance on 321-Avoiding Permutations
Ron M. Adin, Yuval Roichman
Let be the set of 321-avoiding permutations of order . Two properties of are proved: (1) The {\em last descent} and {\em last index minus one} statistics are equidis…