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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We infer upper and lower bounds on the exponential growth constants$\alpha(\Lambda)$, $\alpha_0(\Lambda)$, and $\beta(\Lambda)$ describing thelarge-$n$ behavior of, respectively, the number of acyclic orientations,acyclic orientations with a unique source vertex, and totally cyclicorientations of arrows on bonds of several $n$-vertex heteropolygonalArchimedean lattices $\Lambda$. These are, to our knowledge, the best bounds onthese growth constants. The inferred upper and lower bounds on the growthconstants are quite close to each other, which enables us to derive ratheraccurate values for the actual exponential growth constants. Combining our newresults for heteropolygonal Archimedean lattices with our recent results forhomopolygonal Archimedean lattices, we show that the exponential growthconstants $\alpha(\Lambda)$, $\alpha_0(\Lambda)$, and $\beta(\Lambda)$ on theselattices are monotonically increasing functions of the lattice coordinationnumber. Comparisons are made with the corresponding growth constants forspanning trees on these lattices. Our findings provide further support for theMerino-Welsh and Conde-Merino conjectures.

Study of Exponential Growth Constants of Directed Heteropolygonal Archimedean Lattices