patterns and a classification of the Mahonian statistics.
1]), and the generalized permutation group is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Our first goal is to generalize such properties to the case of generalized permutations.
A generalized permutation is defined to be a biword:
The integer n is called the length of the generalized permutation [alpha].
A generalized involution will be a generalized permutation a satisfying the further condition that each pair [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] occurs as many times as the pair [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
We associate a generalized permutation with a pair (P, Q) of dual semistandard tableaux as follows.
In other words, [alpha] is a Baxter permutation if it avoids the generalized permutation
patterns 2 - 41 - 3 and 3 - 14 - 2 (see  for an introduction on generalized permutation
Steingrimsson: Generalized permutation
patterns--a short survey, Permutation Patterns, St Andrews 2007, S.
Steingrimsson, Generalized permutation
patterns and a classification of the Mahonian statistics, Sem.
To our knowledge the above theorem is the first result of this type for generalized permutation
patterns of length larger than two.
On log surfaces Osamu Fujino and Hiromu Tanaka Zeta functions of generalized permutations
with application to their factorization formulas Shin-ya Koyama and Sachiko NAKAJIMA Above two, communicated by Shigefumi Mori, M.