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

Given a finite, simple, vertex-weighted graph, we construct a gradedassociative (non-commutative) algebra, whose generators correspond to verticesand whose ideal of relations has generators that are graded commutatorscorresponding to edges. We show that the Hilbert series of this algebra is theinverse of the clique polynomial of the graph. Using this result it easy torecognize if the ideal is inert, from which strong results on the algebrafollow. Non-commutative Grobner bases play an important role in our proof.  There is an interesting application to toric topology. This algebra arisesnaturally from a partial product of spheres, which is a special case of ageneralized moment-angle complex. We apply our result to the loop-spacehomology of this space.

Graph products of spheres, associative graded algebras and Hilbert series