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

In 2011 Eriko Hironaka introduced an interesting generalization of Coxetergroups, motivated by studying certain mapping classes. The generalization is bylabeling the vertices of a Coxeter graph either by +1 or by -1, and thengeneralizing the standard geometric representation of the associated Coxetergroup by concerning the labels of the vertices. The group which Hironaka get bythat generalization is called mixed-sign Coxeter group. In this paper weclassify the simply-laced mixed-sign Coxeter groups where the associated graphis either a line or a simple cycle. We show that all the defining relations ofthe mixed-sign Coxeter groups with the mentioned associated graph (either aline or a simple cycle) are squares or cubes of a product of conjugates of twogenerators of the mixed-sign Coxeter group and are strongly connected to thelabels of the vertices of the associated graph.

Simply-laced mixed-sign Coxeter groups, with an associate graph is a line or a simple cycle