Pattern frequency sequences and internal zeros

Bona, Miklos; Sagan, Bruce; Vatter, Vincent

Pattern frequency sequences and internal zeros

Authors

Bona, Miklos

Sagan, Bruce

Vatter, Vincent

Description

Consider the number of permutations in the symmetric group on n letters that contain c copies of a given pattern. As c varies (with n held fixed) these numbers form a sequence whose properties we study for the monotone patterns and the patterns 1, l, l-1, ..., 2. We show that, except for the patterns 1, 2 and 2, 1 where the sequence is well-known to be log concave, there are infinitely many n where the sequence has internal zeros.
24 pages