A Language-Theoretic Approach to the Heapability of Signed Permutations

TL;DR

This paper explores a signed variant of the Hammersley process, characterizing the words it produces and showing that this language is the intersection of two deterministic one-counter languages, advancing understanding of heapability in signed sequences.

Contribution

It introduces a signed version of the Hammersley process and provides a characterization of its image language as the intersection of two deterministic one-counter languages.

Findings

Characterization of words generated by the signed Hammersley process

The language of these words is the intersection of two deterministic one-counter languages

Provides insights into heapability of signed sequences

Abstract

We investigate a signed version of the Hammersley process, a discrete process on words related to a property of integer sequences called heapability (Byers et al., ANALCO 2011). The specific version that we investigate corresponds to a version of this property for signed sequences. We give a characterization of the words that can appear as images the signed Hammersley process. In particular we show that the language of such words is the intersection of two deterministic one-counter languages.