A permutation of n letters is k-prolific if each (n - k)-subset of the letters in its one-line notation forms a unique pattern. We present a complete characterization of k-prolific permutations for each k, proving that k-prolific permutations of m letters exist for every m >= k^2/2+2k+1, and that none exist of smaller size. Key to these results is a natural bijection between k-prolific permutations and certain "permuted" packings of diamonds.
|Number of pages||24|
|Journal||Journal of Combinatorial Theory Series A|
|Early online date||1 Sept 2017|
|Publication status||Published - 31 Jan 2018|
- pattern poset
- prolific permutation
- permuted packing