Optimizing Linear Extensions

TL;DR

This paper investigates bounds on the size of posets required to have a specific number of linear extensions, providing improved bounds in certain cases to better understand their structure.

Contribution

It establishes new upper bounds on the size of posets with a given number of linear extensions, including an improved bound for a special case.

Findings

Maximum size of posets with n linear extensions is at most 2sqrt{n}.

In a special case, the size bound improves to sqrt{n}.

Provides theoretical bounds on poset structures.

Abstract

The minimum number of elements needed for a poset to have exactly n linear extensions is at most 2sqrt{n}. In a special case, the bound can be improved to sqrt{n}.