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 Plus

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

Zendy Tools

Zendy Open

It is well known that the number of tilting modules over a path algebra oftype A_n coincides with the Catalan number C(n). Moreover, the number ofsupport tilting modules of type A_n is the Catalan number C(n+1). We show thatthe convex hull of all roots of a root system of type A_n is a polytope withintegral volume (n + 1)C(n+1). Moreover, we associate to the set of tiltingmodules and to the set of support tilting modules certain polytopes and showthat their volumes coincide with the number of those modules, respectively.Finally, we show that these polytopes can be defined just using the root systemand relate their volumes, so that we can derive the above results in a new way.

Tilting Modules over the Path Algebra of Type A, Polytopes, and Catalan Numbers