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Blocks in cycles and k-commuting permutations.

Rutilo Moreno1, Luis Manuel Rivera2

  • 1Instituto de Física, Universidad Autónoma de San Luis Potosí, San Luis Potosí, Mexico.

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|November 25, 2016
PubMed
Summary
This summary is machine-generated.

We introduce k-commuting permutations, providing a characterization for permutations that k-commute with a given permutation. This leads to formulas for counting such permutations, connecting to known integer sequences.

Keywords:
Commutation relationEnumerationHamming metricSymmetric group

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Area of Science:

  • Combinatorics
  • Abstract Algebra
  • Permutation Group Theory

Background:

  • Permutations are fundamental objects in mathematics.
  • Understanding permutation commutation properties is crucial in various algebraic structures.
  • The study of k-commuting permutations extends existing concepts.

Purpose of the Study:

  • To introduce and formally define k-commuting permutations.
  • To characterize permutations that k-commute with a given permutation.
  • To derive formulas for enumerating k-commuting permutations for specific cycle types.

Main Methods:

  • Development of a characterization theorem for k-commuting permutations.
  • Application of combinatorial techniques for enumeration.
  • Comparison of results with existing integer sequences.

Main Results:

  • A precise characterization of permutations exhibiting k-commutation.
  • Formulas for the number of k-commuting permutations for certain permutation structures.
  • Identification of connections between these results and established integer sequences.

Conclusions:

  • The study establishes a new concept of k-commuting permutations.
  • The derived formulas offer insights into the enumeration of these permutations.
  • New interpretations for certain integer sequences are provided through this research.