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3AP-free permutations have no exponential growth rate

Boon Suan Ho

Abstract

Let $θ(n)$ be the number of permutations of $\{1,\dots,n\}$ with no $3$-term arithmetic progressions. We prove that $\lim_{n\to\infty}θ(n)^{1/n}$ does not exist.

3AP-free permutations have no exponential growth rate

Abstract

Let be the number of permutations of with no -term arithmetic progressions. We prove that does not exist.
Paper Structure (3 sections, 3 theorems, 16 equations)

This paper contains 3 sections, 3 theorems, 16 equations.

Table of Contents

  1. Introduction
  2. The proof
  3. Discussion

Key Result

Theorem 1

$\lim_{n\to\infty}\theta(n)^{1/n}$ does not exist.

Theorems & Definitions (4)

  • Theorem 1
  • Lemma 1: DEGS77
  • proof
  • Lemma 2: Sha09, Theorem 2.8