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/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

In this paper, we consider the generalization of chordal graphs to cluttersproposed by Bigdeli, et al in J. Combin. Theory, Series A (2017). Assume that$\mathcal{C}$ is a $d$-dimensional uniform clutter. It is known that if$\mathcal{C}$ is chordal, then $I(\bar{\mathcal{C}})$ has a linear resolutionover all fields. The converse has recently been rejected, but the followingquestion which poses a weaker version of the converse is still open: "if$I(\bar{\mathcal{C}})$ has linear quotients, is $\mathcal{C}$ necessarilychordal?". Here, by introducing the concept of the ascent of a clutter, wesplit this question into two simpler questions and present some clues insupport of an affirmative answer. In particular, we show that if$I(\bar{\mathcal{C}})$ is the Stanley-Reisner ideal of a simplicial complexwith a vertex decomposable Alexander dual, then $\mathcal{C}$ is chordal.

Chordality of Clutters with Vertex Decomposable Dual and Ascent of Clutters