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

Reiner-Stanton-White defined the cyclic sieving phenomenon (CSP) associatedto a finite cyclic group action and a polynomial. A key example arises from thelength generating function for minimal length coset representatives of aparabolic quotient of a finite Coxeter group. In type A, this result can bephrased in terms of the natural cyclic action on words of fixed content.  There is a natural notion of refinement for many CSP's. We formulate andprove a refinement, with respect to the major index statistic, of this CSP onwords of fixed content by also fixing the cyclic descent type. The argumentpresented is completely different from Reiner-Stanton-White'srepresentation-theoretic approach. It is combinatorial and largely, though notentirely, bijective in a sense we make precise with a "universal" sievingstatistic on words, "flex".  A building block of our argument involves cyclic sieving for shifted subsetsums, which also appeared in Reiner-Stanton-White. We give an alternate,largely bijective proof of a refinement of this result by extending some ideasof Wagon-Wilf.

Refined Cyclic Sieving on Words for the Major Index Statistic