Self-descriptive Sequences directed by two Periodic Sequences

TL;DR

This paper introduces a class of self-descriptive sequences with explicitly computable frequencies, demonstrating that a specific sequence from prior work has the expected frequencies of occurrences.

Contribution

It provides a new class of self-descriptive sequences with explicit frequency calculations and confirms the frequency properties of a sequence from previous research.

Findings

Explicitly computed frequencies for the new class of sequences

Proof that a known sequence has expected frequencies

Sequences can be explicitly constructed and analyzed

Abstract

In the present work, we exhibit a class of self-descriptive sequences that can be explicitly computed and whose frequencies are known. In particular, as a corollary of our main result, we prove that the sequence introduced in \citeBJM23 has the expected frequencies of occurrences.