Strongly Cancellative and Recovering Sets On Lattices

TL;DR

This paper employs information theory to analyze and establish bounds for recovering and strongly cancellative sets on specific lattices, advancing understanding of their structure and limitations.

Contribution

It introduces new bounds and constructions for recovering and cancellative sets on lattices like B_n and D_{l}^{k}, expanding prior theoretical frameworks.

Findings

Upper bounds for recovering sets on B_n and D_{l}^{k}

Constructive methods for strongly cancellative sets

Enhanced understanding of set properties on lattices

Abstract

We use information theory to study recovering sets $\R_L$ and strongly cancellative sets $\C_L$ on different lattices. These sets are special classes of recovering pairs and cancellative sets previously discussed in [1], [3] and [5]. We mainly focus on the lattices $B_n$ and $D_{l}^{k}$. Specifically, we find upper bounds and constructions for the sets $\R_{B_n}$, $\C_{B_n}$, and $\C_{D_{l}^{k}}$.