Subspaces, subsets, and Motzkin paths

TL;DR

This paper introduces a novel mapping from subspaces to Motzkin paths, revealing a symmetric Boolean decomposition of the subspace lattice through inverse images.

Contribution

It presents an explicit construction linking subspaces and Motzkin paths, providing new combinatorial insights into the structure of the subspace lattice.

Findings

Mapped subspaces to Motzkin paths

Decomposed subspace lattice into symmetric Boolean subsets

Established a bijective correspondence between paths and lattice subsets

Abstract

We define a map from subspaces to Motzkin paths and show that the inverse image of every path is a disjoint union of symmetric Boolean subsets yielding an explicit symmetric Boolean decomposition of the subspace lattice.