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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

For an ad-nilpotent ideal $i$ of a Borel subalgebra of $sl_{l+1}(C)$, wedenote by $I_i$ the maximal subset $I$ of the set of simple roots such that $i$is an ad-nilpotent ideal of the standard parabolic subalgebra $p_I$. We use thebijection given by G.E. Andrews, C. Krattenthaler, L. Orsina and P. Papibetween the set of ad-nilpotent ideals of a Borel subalgebra in $sl_{l+1}(C)$and the set of Dyck paths of length $2l+2$, to explicit a bijection betweenad-nilpotent ideals $i$ of the Borel subalgebra such that the cardinality of$I_i$ is equal to $r$ and the Dyck paths of length $2l+2$ having $r$ occurence"udu". We obtain also a duality between antichains of cardinality $p$ and $l-p$in the set of positive roots.

Number of "udu" of a Dyck path and ad-nilpotent ideals of parabolic subalgebras of sl_{l+1}(C)