Generating and Enumerating 321-Avoiding and Skew-Merged Simple Permutations
نویسندگان
چکیده
منابع مشابه
Generating and Enumerating 321-Avoiding and Skew-Merged Simple Permutations
The simple permutations in two permutation classes — the 321-avoiding permutations and the skew-merged permutations — are enumerated using a uniform method. In both cases, these enumerations were known implicitly, by working backwards from the enumeration of the class, but the simple permutations had not been enumerated explicitly. In particular, the enumeration of the simple skew-merged permut...
متن کاملSkew-merged Simple Permutations
The simple permutations in two permutation classes — the 321-avoiding permutations and the skew-merged permutations — are enumerated using a uniform method. In both cases, these enumerations were known implicitly, by working backwards from the enumeration of the class, but the simple permutations had not been enumerated explicitly. In particular, the enumeration of the simple skew-merged permut...
متن کاملThe Complexity of Pattern Matching for 321-Avoiding and Skew-Merged Permutations
The PERMUTATION PATTERNMATCHING problem, asking whether a pattern permutation π is contained in a permutation τ, is known to be NPcomplete. In this paper we present two polynomial time algorithms for special cases. The first algorithm is applicable if both π and τ are 321avoiding; the second is applicable if π and τ are skew-merged. Both algorithms have a runtime of Opknq, where k is the length...
متن کامل321-Polygon-Avoiding Permutations and Chebyshev Polynomials
A 321-k-gon-avoiding permutation π avoids 321 and the following four patterns: k(k + 2)(k + 3) · · · (2k − 1)1(2k)23 · · · (k − 1)(k + 1), k(k + 2)(k + 3) · · · (2k − 1)(2k)12 · · · (k − 1)(k + 1), (k + 1)(k + 2)(k + 3) · · · (2k − 1)1(2k)23 · · · k, (k + 1)(k + 2)(k + 3) · · · (2k − 1)(2k)123 · · · k. The 321-4-gon-avoiding permutations were introduced and studied by Billey and Warrington [BW]...
متن کاملThe Fine Structure of 321 Avoiding Permutations. the Fine Structure of 321 Avoiding Permutations
Bivariate generating functions for various subsets of the class of permutations containing no descending sequence of length three or more are determined. The notion of absolute indecomposability of a permutation is introduced, and used in enumerating permutations which have a block structure avoiding 321, and whose blocks also have such structure (recursively). Generalizations of these results ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2013
ISSN: 1077-8926
DOI: 10.37236/3058