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On the inverse Mobius transformation and unrestricted partitions

Romulo Leoncio Cruz Simbron

Abstract

In this work we explore the relationship between the Mobius inverse transformation of an arbitrary sequence and unrestricted partitions identities.

On the inverse Mobius transformation and unrestricted partitions

Abstract

In this work we explore the relationship between the Mobius inverse transformation of an arbitrary sequence and unrestricted partitions identities.
Paper Structure (3 sections, 6 theorems, 43 equations)

This paper contains 3 sections, 6 theorems, 43 equations.

Table of Contents

  1. Introduction
  2. Arithmetical interpretation of weighted partitions identities related to the largest and smallest part
  3. Proof of the Theorems and Corollaries

Key Result

Theorem 1

Let $a_n$ an arbitrary sequence of real or imaginary terms, $n$ a positive integer number, and $t$ and $u$ real or imaginary numbers. Then where $s(\pi)$ is the smallest term in the partitions $\pi$

Theorems & Definitions (15)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Corollary 1
  • Corollary 2
  • Example 1
  • Example 2
  • Example 3
  • proof
  • ...and 5 more