The Endomorphism Conjecture for Graded Posets of Width 4

TL;DR

This paper proves the endomorphism conjecture for graded posets with width up to 4, confirming the conjecture for a significant class of posets and advancing understanding in order theory.

Contribution

It establishes the endomorphism conjecture for all graded posets of width at most 4, extending previous partial results in the field.

Findings

Endomorphism conjecture holds for graded posets of width 4

Proof techniques applicable to posets with Whitney number up to 4

Confirms the conjecture for a broad class of graded posets

Abstract

We prove the endomorphism conjecture for graded posets whose largest Whitney number is at most 4. In particular, this implies the endomorphism conjecture is true for graded posets of width at most 4.