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

We introduce a new statistic, skip, on rational $(3,n)$-Dyck paths and definea marked rank word for each path when $n$ is not a multiple of 3. If a tripleof valid statistics (area,skip,dinv) are given, we have an algorithm toconstruct the marked rank word corresponding to the triple. By considering allvalid triples we give an explicit formula for the $(m,n)$-rational$q,t$-Catalan polynomials when $m=3$. Then there is a natural bijection on thetriples of statistics (area,skips,dinv) which exchanges the statistics area anddinv while fixing the skip. Thus we prove the $q,t$-symmetry of$(m,n)$-rational $q, t$-Catalan polynomials for $m=3$.

The $(m,n)$-rational $q, t$-Catalan polynomials for $m=3$ and their $q,t$-symmetry