Category: Permutation patterns

In the mathematical study of permutations and permutation patterns, a superpattern or universal permutation is a permutation that contains all of the patterns of a given length. More specifically, a k
Stanley–Wilf conjecture
The Stanley–Wilf conjecture, formulated independently by Richard P. Stanley and Herbert Wilf in the late 1980s, states that the growth rate of every proper permutation class is singly exponential. It
Layered permutation
In the mathematics of permutations, a layered permutation is a permutation that reverses contiguous blocks of elements. Equivalently, it is the direct sum of decreasing permutations. One of the earlie
Enumerations of specific permutation classes
In the study of permutation patterns, there has been considerable interest in enumerating specific permutation classes, especially those with relatively few basis elements. This area of study has turn
Permutation class
In the study of permutations and permutation patterns, a permutation class is a set of permutations such that every pattern within a permutation in is also in . In other words, a permutation class is
Separable permutation
In combinatorial mathematics, a separable permutation is a permutation that can be obtained from the trivial permutation 1 by direct sums and skew sums. Separable permutations may be characterized by
Vexillary permutation
In mathematics, a vexillary permutation is a permutation μ of the positive integers containing no subpermutation isomorphic to the permutation (2143); in other words, there do not exist four numbers i
Permutation pattern
In combinatorial mathematics and theoretical computer science, a permutation pattern is a sub-permutation of a longer permutation. Any permutation may be written in one-line notation as a sequence of
Riffle shuffle permutation
In the mathematics of permutations and the study of shuffling playing cards, a riffle shuffle permutation is one of the permutations of a set of items that can be obtained by a single riffle shuffle,
Wilf equivalence
In the study of permutations and permutation patterns, Wilf equivalence is an equivalence relation on permutation classes.Two permutation classes are Wilf equivalent when they have the same numbers of
Erdős–Szekeres theorem
In mathematics, the Erdős–Szekeres theorem asserts that, given r, s, any sequence of distinct real numbers with length at least (r − 1)(s − 1) + 1 contains a monotonically increasing subsequence of le
Skew-merged permutation
In the theory of permutation patterns, a skew-merged permutation is a permutation that can be partitioned into an increasing sequence and a decreasing sequence. They were first studied by and given th
Stack-sortable permutation
In mathematics and computer science, a stack-sortable permutation (also called a tree permutation) is a permutation whose elements may be sorted by an algorithm whose internal storage is limited to a
Baxter permutation
In combinatorial mathematics, a Baxter permutation is a permutation which satisfies the following generalized pattern avoidance property: * There are no indices i < j < k such that σ(j + 1) < σ(i) <
Gilbreath shuffle
A Gilbreath shuffle is a way to shuffle a deck of cards, named after mathematician Norman Gilbreath (also known for Gilbreath's conjecture). Gilbreath's principle describes the properties of a deck th