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SUPERPATTERN

Superpattern

a superpattern or universal permutation is a permutation that contains all of the patterns of a given length. More specifically, a k-superpattern contains

Superpattern

Superpermutation

String in combinatorial math

current best lower bound (see section above) for n = 7 is still 5884. Superpattern, a permutation that contains each permutation of n symbols as a permutation

Superpermutation

Permutation pattern

Subpermutation of a longer permutation

packing density. A k-superpattern is a permutation that contains all permutations of length k. For example, 25314 is a 3-superpattern because it contains

Permutation pattern

Permutation_pattern

Layered permutation

by the same function 2 n − 1 {\displaystyle 2^{n-1}} . The shortest superpattern of the layered permutations of length n {\displaystyle n} is itself a

Layered permutation

Layered_permutation

Permutation

Mathematical version of an order change

group) Probability Rencontres numbers Sorting network Substitution cipher Superpattern Superpermutation Twelvefold way Weak order of permutations 1 is frequently

Permutation

List of permutation topics

permutation Parity of a permutation Separable permutation Stirling permutation Superpattern Transposition (mathematics) Unpredictable permutation Bijection Combination

List of permutation topics

List_of_permutation_topics

Sorting number

Worst-case number of comparisons used by sorting algorithms

(shifted by one position) also give the sizes of the shortest possible superpatterns for the layered permutations. Ford, Lester R. Jr.; Johnson, Selmer M

Sorting number

Sorting_number

Richard Arratia

American mathematician

convergence of a limit, and was the first to investigate the lengths of superpatterns of permutations. He has also written highly cited papers on the Chen–Stein

Richard Arratia

Richard_Arratia

Universal point set

Points usable to draw any planar graph

point sets are not based on grids, but are instead constructed from superpatterns (permutations that contain all permutation patterns of a given size);

Universal point set

Universal_point_set