Characterization of the allowed patterns of signed shifts

TL;DR

This paper characterizes the allowed permutation patterns of signed shift maps, providing a comprehensive understanding of their combinatorial structure and bounds on their enumeration.

Contribution

It introduces a complete characterization and bounds for the allowed patterns of signed shift maps, expanding the understanding of their combinatorial properties.

Findings

Characterization of allowed patterns for signed shifts

Enumerative bounds for these patterns

Enhanced understanding of the combinatorial structure

Abstract

The allowed patterns of a map are those permutations in the same relative order as the initial segments of orbits realized by the map. In this paper, we characterize and provide enumerative bounds for the allowed patterns of signed shifts, a family of maps on infinite words.