Year: 2003
Type: preprint
Abstract: Natural q analogues of classical statistics on the symmetric groups $S_n$ are introduced; parameters like: the q-length, the q-inversion number, the q-descent number and the q-major index. MacMahon's theorem about the equi-distribution of the inversion number and the reverse major index is generalized to all positive integers q. It is also shown that the q-inversion number and the q-reverse major index are equi-distributed over subsets of permutations avoiding certain patterns. Natural q analogues of the Bell and the Stirling numbers are related to these q statistics -- through the counting of the above pattern-avoiding permutations.
Source: arXiv (Cornell University)
Authors: Regev, Amitai, Roichman, Yuval
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1643265384