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

Regular $A_n$-, $B_n$- and $C_n$-crystals are edge-colored directed graphs,with ordered colors $1,2,...,n$, which are related to representations ofquantized algebras $U_q(\mathfrak{sl}_{n+1})$, $U_q(\mathfrak{sp}_{2n})$ and$U_q(\mathfrak{so}_{2n+1})$, respectively. We develop combinatorial methods toreveal refined structural properties of such objects.  Firstly, we study subcrystals of a regular $A_n$-crystal $K$ and characterizepairwise intersections of maximal subcrystals with colors $1,...,n-1$ andcolors $2,...,n$. This leads to a recursive description of the structure of $K$and provides an efficient procedure of assembling $K$.  Secondly, using merely combinatorial means, we demonstrate a relationshipbetween regular $B_n$-crystals (resp. $C_n$-crystals) and regular symmetric$A_{2n-1}$-crystals (resp. $A_{2n}$-crystals).

On the combinatorial structure of crystals of types A,B,C