منابع مشابه
Packing sets of patterns
Packing density is a permutation occurrence statistic which describes the maximal number of permutations of a given type that can occur in another permutation. In this article we focus on containment of sets of permutations. Although this question has been tangentially considered previously, this is the first systematic study of it. We find the packing density for various special sets of permut...
متن کاملPacking Densities of Patterns
The packing density of a permutation π of length n is the maximum proportion of subsequences of length n which are order-isomorphic to π in arbitrarily long permutations σ. For the generalization to patterns π which may have repeated letters, two notions of packing density have been defined. In this paper, we show that these two definitions are equivalent, and we compute the packing density for...
متن کاملPacking Patterns into Words
In this article we generalize packing density problems from permutations to patterns with repeated letters and generalized patterns. We are able to find the packing density for some classes of patterns and several other short patterns. A string 213322 contains three subsequences 233, 133, 122 each of which is orderisomorphic (or simply isomorphic) to the string 122, i.e. ordered in the same way...
متن کاملDense Packing of Patterns in a Permutation
We study the length Lk of the shortest permutation containing all patterns of length k. We establish the bounds e−2k2 < Lk ≤ (2/3 + o(1))k2 . We also prove that as k → ∞, there are permutations of length (1/4+o(1))k2 containing almost all patterns of length k.
متن کاملNote on Packing Patterns in Colored Permutations
Packing patterns in permutations concerns finding the permutation with the maximum number of a prescribed pattern. In 2002, Albert, Atkinson, Handley, Holton and Stromquist showed that there always exists a layered permutation containing the maximum number of a layered pattern among all permutations of length n. Consequently the packing density for all but two (up to equivalence) patterns up to...
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ژورنال
عنوان ژورنال: Acta Crystallographica Section A Foundations of Crystallography
سال: 2000
ISSN: 0108-7673
DOI: 10.1107/s010876730002643x