Pattern frequency sequences and internal zeros

Miklos Bona; Bruce Sagan; Vincent Vatter

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arXiv · math/0104098

Pattern frequency sequences and internal zeros

Miklos Bona·Bruce Sagan·Vincent Vatter

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Abstract

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.

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Miklos Bona, Bruce Sagan, Vincent Vatter. 2001-04-08. Pattern frequency sequences and internal zeros. https://arxiv.org/abs/math/0104098

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