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Alternating permutation: André's theorem, Seidel's Algorithm & Related sequences

In combinatorial mathematics, an alternating permutation (or zigzag permutation) of the set {1, 2, 3, ..., n} is a permutation (arrangement) of those numbers so that each entry is alternately greater or less than the preceding entry. For example, the five alternating permutations of {1, 2, 3, 4} are:

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Alternating permutation topic overview

The analysis highlights André's theorem, Seidel's Algorithm and Related sequences as prominent areas in the source structure around Alternating permutation.

Related topics
34
Source areas
6
Connected nodes
40
Extracted relationships
21
Concept neighborhoods
23
Bridge connections
40

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

André's theorem · 15 topics
Seidel's Algorithm · 7 topics
Overview · 5 topics
Related sequences · 3 topics
Definitions · 2 topics
Explicit formula in terms of Stirling numbers of the second kind · 2 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Definitions

André's theorem

Seidel's Algorithm

Related sequences

Explicit formula in terms of Stirling numbers of the second kind

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Alternating permutation connects Entity context

The extracted context around Alternating permutation shows recurring relationship patterns in the source. For example, Alternating permutation → Alternating Permutations, An, An Explicit Formula, Eric, Euler, MathWorld, Richard, Ross Tang, Stanley, Survey, Up/down, Weisstein Another extracted example is Alternating permutation → A000111, An, André's, Catalan, Euler, OEIS, The, These. Use these groups to spot repeated connection types before inspecting the individual relationships.

Alternating permutation

Top relations

related to External links · 12
Alternating permutation → Alternating Permutations, An, An Explicit Formula, Eric, Euler, MathWorld, Richard, Ross Tang, Stanley, Survey, Up/down, Weisstein
related to André's theorem · 8
Alternating permutation → A000111, An, André's, Catalan, Euler, OEIS, The, These
see also · 1
Alternating permutation → Longest

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

oeis first alternating numbers permutations permutation euler zigzag entry sequence set number second andré's tangent values algorithm secant odd 16

Alternating permutation relationships Subject–Predicate–Object triples

TTTA extracted 21 structured relationships around Alternating permutation. Examples in this analysis include Alternating permutation → related to André's theorem → The and Alternating permutation → related to André's theorem → An. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Alternating permutationrelated to André's theoremThe0.60section
Alternating permutationrelated to André's theoremAn0.60section
Alternating permutationrelated to André's theoremAndré's0.60section
Alternating permutationrelated to André's theoremEuler0.60section
Alternating permutationrelated to André's theoremA0001110.60section
Alternating permutationrelated to André's theoremOEIS0.60section
Alternating permutationrelated to André's theoremThese0.60section
Alternating permutationrelated to André's theoremCatalan0.60section
Alternating permutationrelated to External linksWeisstein0.60section
Alternating permutationrelated to External linksEric0.60section
Alternating permutationrelated to External linksMathWorld0.60section
Alternating permutationrelated to External linksRoss Tang0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Alternating permutation bring nearby vocabulary together. In this analysis, examples include Permutations, Set and Permutation. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Alternating permutation
    • Permutations
    • Set
    • Permutation
    • Entry
    • Down-up
    • Up-down
    • André's
    • Numbers
    • Called
    • Name
    • Formula
    • Simple
  • alternating permutation
    • Permutations
    • Set
    • Permutation
    • Entry
    • Down-up
    • Second
    • Up-down
    • André's
    • Numbers
    • Called
    • Name
    • Formula
  • euler numbers
    • Zigzag
    • Euler
    • Numbers
    • Related
    • Bernoulli
    • Formula
    • Simple
    • Tangent
    • Known
    • Called
    • Kind
    • Odd
  • catalan numbers
    • Zigzag
    • Euler
    • Related
    • Bernoulli
    • Formula
    • Simple
    • Tangent
    • Called
    • Kind
    • Known
    • Odd
    • Secant
  • bernoulli numbers
    • Zigzag
    • Euler
    • Related
    • Bernoulli
    • Formula
    • Numbers
    • Simple
    • Tangent
    • Called
    • Kind
    • Known
    • Odd
  • stirling numbers of the second kind
    • Zigzag
    • Euler
    • Kind
    • Second
    • Related
    • Bernoulli
    • Formula
    • Simple
    • Tangent
    • A122045
    • A163747
    • Seidel's
  • explicit formula in terms of stirling numbers of the second kind
    • Zigzag
    • Euler
    • Kind
    • Second
    • Related
    • Secant
    • Tangent
    • Bernoulli
    • Formula
    • Numbers
    • Simple
    • A122045
  • andré's theorem
    • André's
    • Theorem
    • Called
    • Number
    • Set
    • Even
    • Function
    • Kind
    • Known
    • Odd
    • Permutations
    • Secant

Connections between topic areas Semantic bridges

For Alternating permutation, one of the stronger structural bridges in this analysis connects Alternating permutation with André's theorem. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Alternating permutation — André's theorem · splits 25 ⟂ 16
Alternating permutation — Seidel's Algorithm · splits 33 ⟂ 8
Alternating permutation — Overview · splits 35 ⟂ 6
Alternating permutation — Related sequences · splits 37 ⟂ 4
Alternating permutation — Definitions · splits 38 ⟂ 3
Alternating permutation — Explicit formula in terms of Stirling numbers of the second kind · splits 38 ⟂ 3

Map overview Semantic statistics

Alternating permutation

Nodes41
Edges40
Triples21
Avg. degree1.95
Density0.04878
Components1

Source & methodology

TTTA analyzes the structure around Alternating permutation to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as André's theorem, Seidel's Algorithm & Related sequences, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Alternating permutation · EN edition · Analysis: TopicsToTalkAbout

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