Pattern Frequency Sequences and Internal Zeros
نویسندگان
چکیده
Let q be a pattern and let Sn q c be the number of n-permutations having exactly c copies of q. We investigate when the sequence Sn q c c≥0 has internal zeros. If q is a monotone pattern it turns out that, except for q = 12 or 21, the nontrivial sequences (those where n is at least the length of q) always have internal zeros. For the pattern q = 1 l + 1 l 2 there are infinitely many sequences which contain internal zeros and when l = 2 there are also infinitely many which do not. In the latter case, the only possible places for internal zeros are the next-to-last or the second-to-last positions. Note that by symmetry this completely determines the existence of internal zeros for all patterns of length at most 3. 2002 Elsevier Science (USA)
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