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Separable permutation

Index 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. [1]

30 relations: Algebraic geometry, Binary tree, Bootstrap percolation, Cograph, Combinatorics, Discrete Mathematics (journal), Forbidden graph characterization, Generating function, Induced path, Information Processing Letters, Inversion (discrete mathematics), Lowest common ancestor, NP-completeness, Order dimension, Partially ordered set, Permutation, Permutation graph, Permutation matrix, Permutation pattern, Schröder number, Series-parallel partial order, SIAM Journal on Discrete Mathematics, Skew and direct sums of permutations, Springer Science+Business Media, Stack (abstract data type), Stack-sortable permutation, Time complexity, Tree rotation, Very-large-scale integration, Von Neumann neighborhood.

Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

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Binary tree

In computer science, a binary tree is a tree data structure in which each node has at most two children, which are referred to as the and the.

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Bootstrap percolation

In statistical mechanics, bootstrap percolation is a percolation process in which a random initial configuration of active cells is selected from a lattice or other space, and then cells with few active neighbors are successively removed from the active set until the system stabilizes.

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Cograph

In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation and disjoint union.

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Combinatorics

Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.

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Discrete Mathematics (journal)

Discrete Mathematics is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications.

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Forbidden graph characterization

In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to the family and further exclude all graphs from the family which contain any of these forbidden graphs as (induced) subgraph or minor.

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Generating function

In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.

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Induced path

In the mathematical area of graph theory, an induced path in an undirected graph G is a path that is an induced subgraph of G. That is, it is a sequence of vertices in G such that each two adjacent vertices in the sequence are connected by an edge in G, and each two nonadjacent vertices in the sequence are not connected by any edge in G. An induced path is sometimes called a snake, and the problem of finding long induced paths in hypercube graphs is known as the snake-in-the-box problem.

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Information Processing Letters

Information Processing Letters is a peer reviewed scientific journal in the field of computer science, published by Elsevier.

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Inversion (discrete mathematics)

In computer science and discrete mathematics a sequence has an inversion where two of its elements are out of their natural order.

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Lowest common ancestor

In graph theory and computer science, the lowest common ancestor (LCA) of two nodes and in a tree or directed acyclic graph (DAG) is the lowest (i.e. deepest) node that has both and as descendants, where we define each node to be a descendant of itself (so if has a direct connection from, is the lowest common ancestor).

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NP-completeness

In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.

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Order dimension

In mathematics, the dimension of a partially ordered set (poset) is the smallest number of total orders the intersection of which gives rise to the partial order.

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Partially ordered set

In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.

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Permutation

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.

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Permutation graph

In mathematics, a permutation graph is a graph whose vertices represent the elements of a permutation, and whose edges represent pairs of elements that are reversed by the permutation.

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Permutation matrix

\pi.

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Permutation pattern

In combinatorial mathematics and theoretical computer science, a permutation pattern is a sub-permutation of a longer permutation.

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Schröder number

In mathematics, a Schröder number S_n, also called a large Schröder number or big Schröder number, describes the number of lattice paths from the southwest corner (0,0) of an n \times n grid to the northeast corner (n,n), using only single steps north, (0,1); northeast, (1,1); or east, (1,0), that do not rise above the SW–NE diagonal.

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Series-parallel partial order

In order-theoretic mathematics, a series-parallel partial order is a partially ordered set built up from smaller series-parallel partial orders by two simple composition operations.

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SIAM Journal on Discrete Mathematics

SIAM Journal on Discrete Mathematics is a peer-reviewed mathematics journal published quarterly by the Society for Industrial and Applied Mathematics (SIAM).

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Skew and direct sums of permutations

In combinatorics, the skew sum and direct sum of permutations are two operations to combine shorter permutations into longer ones.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Stack (abstract data type)

In computer science, a stack is an abstract data type that serves as a collection of elements, with two principal operations.

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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 single stack data structure.

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Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.

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Tree rotation

In discrete mathematics, tree rotation is an operation on a binary tree that changes the structure without interfering with the order of the elements.

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Very-large-scale integration

Very-large-scale integration (VLSI) is the process of creating an integrated circuit (IC) by combining hundreds of thousands of transistors or devices into a single chip.

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Von Neumann neighborhood

In cellular automata, the von Neumann neighborhood is classically defined on a two-dimensional square lattice and is composed of a central cell and its four adjacent cells.

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Separable permutations.

References

[1] https://en.wikipedia.org/wiki/Separable_permutation

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