Strongly Cancellative and Recovering Sets on Lattices

摘要

We use information theory to study recovering sets ${mathbf{R}}_L$ and strongly cancellative sets ${mathbf{C}}_L$ on different lattices. These sets are special classes of recovering pairs and cancellative sets previously discussed in the papers of Simonyi, Frankl, and Füredi. We mainly focus on the lattices $B_n$ and $D_{l}^{k}$. Specifically, we find upper bounds and constructions for the sets ${mathbf{R}}_{B_n}$, ${mathbf{C}}_{B_n}$, and ${mathbf{C}}_{D_{l}^{k}}$.