Pattern Frequency Sequences and Internal Zeros
Copyright policy )Pattern Frequency Sequences and Internal Zeros
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
- University of Florida United States
- University of Florida United States
- Michigan State University United States
- Rutgers, The State University of New Jersey United States
- Michigan State University United States
Permutations, words, matrices, 05A05 (Primary) 05A20, 05E99, 06A07 (Secondary), permutations, Applied Mathematics, Exact enumeration problems, generating functions, FOS: Mathematics, Mathematics - Combinatorics, patterns, Combinatorics (math.CO)
Permutations, words, matrices, 05A05 (Primary) 05A20, 05E99, 06A07 (Secondary), permutations, Applied Mathematics, Exact enumeration problems, generating functions, FOS: Mathematics, Mathematics - Combinatorics, patterns, Combinatorics (math.CO)
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