# The meet operation in the imbalance lattice of maximal instantaneous codes: alternative proof of existence

## TL;DR

This paper presents an alternative proof for the existence of greatest lower bounds in the imbalance order of binary maximal instantaneous codes, using a novel balancing operation instead of traditional methods.

## Contribution

It introduces a new proof technique for the existence of greatest lower bounds in the imbalance lattice of maximal instantaneous codes.

## Key findings

- Proof of existence of greatest lower bounds using a single balancing operation
- Simplifies previous proofs by avoiding expansion and contraction
- Provides a new perspective on the structure of the imbalance lattice

## Abstract

An alternative proof is given of the existence of greatest lower bounds in the imbalance order of binary maximal instantaneous codes of a given size. These codes are viewed as maximal antichains of a given size in the infinite binary tree of 0-1 words. The proof proposed makes use of a single balancing operation instead of expansion and contraction as in the original proof of the existence of glb.