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

Flow polytopes are an important class of polytopes in combinatorics whoselattice points and volumes have interesting properties and relations. TheChan-Robbins-Yuen (CRY) polytope is a flow polytope with normalized volumeequal to the product of consecutive Catalan numbers. Zeilberger proved this byevaluating the Morris constant term identity, but no combinatorial proof isknown. There is a refinement of this formula that splits the largest Catalannumber into Narayana numbers, which M\'esz\'aros gave an interpretation as thevolume of a collection of flow polytopes. We introduce a new refinement of theMorris identity with combinatorial interpretations both in terms of latticepoints and volumes of flow polytopes. Our results generalize M\'esz\'aros'sconstruction and a recent flow polytope interpretation of the Morris identityby Corteel-Kim-M\'esz\'aros. We prove the product formula of our refinementfollowing the strategy of the Baldoni-Vergne proof of the Morris identity.Lastly, we study a symmetry of the Morris identity bijectively using theDanilov-Karzanov-Koshevoy triangulation of flow polytopes and a bijection ofM\'esz\'aros-Morales-Striker.

Refinements and Symmetries of the Morris identity for volumes of flow polytopes