On the imbalance lattice of path-length sequences of binary trees

TL;DR

This paper investigates the structure of the imbalance lattice of binary tree path-length sequences, establishing the existence of greatest lower bounds and characterizing join-irreducible elements based on monotonicity properties.

Contribution

It demonstrates the existence of greatest lower bounds in the imbalance lattice and characterizes join-irreducible sequences, advancing understanding of binary tree imbalance structures.

Findings

Greatest lower bounds exist in the imbalance lattice.

Join-irreducible sequences are characterized.

Monotonicity of expansion operations underpins the lattice structure.

Abstract

The existence of greatest lower bounds in the imbalance order of path-length sequences of binary trees is seen to be a consequence of a joint monotonicity property of the greater and lower expension operations. Path length sequences that are join-irreducible in the imbalance lattice are characterized.