English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

$S$-gap shifts are a well-studied class of shift spaces, which has led toseveral proposed generalizations. This paper introduces a new class of shiftspaces called $\mathcal{S}$-graph shifts whose essential structure is encodedin a novel way, as a finite directed graph with a set of natural numbersassigned to each vertex. $\mathcal{S}$-graph shifts contain $S$-gap shifts andtheir generalizations, as well as all vertex shifts and SFTs, as special cases,thereby providing a method to study these shift spaces in a uniform way. Themain result in this paper is a formula for the entropy of any$\mathcal{S}$-graph shift, which, by specialization, resolves a problemproposed by Matson and Sattler. A second result establishes an explicit formulafor the zeta functions of $\mathcal{S}$-graph shifts. Additionally, we showthat every entropy value is obtained by uncountably many $\mathcal{S}$-graphshifts.

Dynamics and entropy of $\mathcal{S}$-graph shifts