Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Alternating patterns in commutator monomials

Gyula Lakos

Abstract

Considering commutator monomials of the non-commutative associative variables $X_1,\ldots,X_n$; we determine the maximal possible number of alternating associative monomials in their noncommutative polynomial expansions. This is achieved by replacing generating functions with polytope sequences, which turn out to be finitely generated in some sense.

Alternating patterns in commutator monomials

Abstract

Considering commutator monomials of the non-commutative associative variables ; we determine the maximal possible number of alternating associative monomials in their noncommutative polynomial expansions. This is achieved by replacing generating functions with polytope sequences, which turn out to be finitely generated in some sense.
Paper Structure (3 sections, 5 theorems, 314 equations)

This paper contains 3 sections, 5 theorems, 314 equations.

Table of Contents

  1. Introduction and statement of main results
  2. Commutator polytopes and their generating sets
  3. The number of alternating permutations

Key Result

Theorem 1.1

The number $r_n$ is given by the table where $k\in\mathbb N$.

Theorems & Definitions (8)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Theorem 2.1
  • Theorem 2.2
  • Remark 2.3
  • proof : (Sketch of) Proofs.
  • Remark 2.4