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

In earlier work in collaboration with Pavel Galashin and Thomas McConville weintroduced a version of chip-firing for root systems. Our investigation of rootsystem chip-firing led us to define certain polynomials analogous to Ehrhartpolynomials of lattice polytopes, which we termed the symmetric and truncatedEhrhart-like polynomials. We conjectured that these polynomials havenonnegative integer coefficients. Here we affirm "half" of this positivityconjecture by providing a positive, combinatorial formula for the coefficientsof the symmetric Ehrhart-like polynomials. This formula depends on a subtleintegrality property of slices of permutohedra, and in turn a lemma concerningdilations of projections of root polytopes, which both may be of independentinterest. We also discuss how our formula very naturally suggests a conjecturefor the coefficients of the truncated Ehrhart-like polynomials that turns outto be false in general, but which may hold in some cases.

A positive formula for the Ehrhart-like polynomials from root system chip-firing