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The gold partition conjecture and the Lexicographic sum of posets

Eric R. Dolores-Cuenca, Aldo Guzmán-Sáenz, Sangil Kim

Abstract

If a finite poset $Q$ satisfies the Gold Partition Conjecture, and $P$ is a finite poset, then for any $i$ in $P$ the lexicographic sum of $P$ with $Q$ on the point $i$, satisfies the Gold Partition Conjecture.

The gold partition conjecture and the Lexicographic sum of posets

Abstract

If a finite poset satisfies the Gold Partition Conjecture, and is a finite poset, then for any in the lexicographic sum of with on the point , satisfies the Gold Partition Conjecture.

Paper Structure

This paper contains 5 sections, 5 theorems, 10 equations, 1 table.

Table of Contents

  1. Introduction
  2. The lexicographic sum
  3. Locality
  4. Final remarks
  5. Acknowledgements

Key Result

Lemma 1

If $Q$ is a finite poset that satisfies the GPC, and $P$ is a finite poset, then for every $i\in P,$ the lexicographic sum $P\circ_iQ$ satisfies the GPC.

Theorems & Definitions (20)

  • Conjecture 1.1: 1/3-2/3 Conjecture
  • Conjecture 1.2: Gold Partition Conjecture (GPC)
  • Definition 1.3
  • Definition 1.4
  • Definition 1.5
  • Lemma
  • Remark 2.1: Locality of lexicographic sum
  • Definition 2.2
  • Lemma 2.3
  • proof
  • ...and 10 more