Partitioning the Boolean lattice into copies of a poset

TL;DR

This paper proves that for large enough n, the Boolean lattice can be partitioned into copies of any poset P of size 2^k with a greatest and least element, confirming a conjecture by Lonc.

Contribution

It establishes the existence of such partitions for large n, solving a longstanding conjecture in the field.

Findings

Boolean lattice can be partitioned into copies of P for large n

Confirms Lonc's conjecture for posets of size 2^k with extremal elements

Provides a method to partition Boolean lattices into structured subposets

Abstract

Let $P$ be a poset of size $2^k$ that has a greatest and a least element. We prove that, for sufficiently large $n$, the Boolean lattice $2^{[n]}$ can be partitioned into copies of $P$. This resolves a conjecture of Lonc.