标题： 模式频率序列和内部零 显示英文标题

标题： Pattern frequency sequences and internal zeros

摘要： 考虑对称群上n个字母的排列中包含给定模式c次的数量。 当c变化（n保持固定）时，这些数形成一个序列，我们研究单调模式和模式1, l, l-1, ..., 2的性质。 我们证明，除了模式1, 2和2, 1外，序列已知是log concave，存在无限多个n使得序列有内部零。 显示英文摘要

摘要： 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.