Deleting digits

TL;DR

This paper explores the minimal elements under a special ordering of positive integers, extending previous work by computing minimal sets for various interesting sets and discussing their properties.

Contribution

It generalizes Shallit's earlier results by analyzing minimal sets for new arithmetically interesting sets and examining their size and shape.

Findings

Computed minimal sets for several new integer subsets

Discussed the size and shape characteristics of minimal sets

Extended understanding of the special ordering in number theory

Abstract

In 2000, J. Shallit introduced a special partial ordering of a subset of positive integers and proposed the problem of finding the set of minimal elements with respect to this ordering. Shallit himself solved this problem for the set of primes and also for the set of composite numbers. In this recreational mathematics note, we compute the minimal sets of a few other arithmetically interesting sets and discuss questions on size and shape of minimal sets in general.