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 this note, we apply combinatorial techniques from our Ph.D. thesis tostudy how generalized permutohedra may be represented functionally onParke-Tayor factors and related rational functions. In any functionalrepresentation of polyhedral cones, in general certain homological informationmay be lost. The combinatorial relations of the Parke-Taylor factors lifthomologically to generalized permutohedra.  The 6-particle case contains several related layers of interesting geometricdata: the Newton polytope for the polynomial numerator lifts the permutohedronin three variables, which is a hexagon, and the fraction itself provides afunctional representation of certain neighborhoods of a vertex of a5-dimensional weight permutohedron. The lift from fraction to generalizedpermutohedron was derived by comparing functional representations. We observeadditionally that the numerator and its permutations satisfy a degree 3polynomial relation which defines a classical projective variety known as theSegre cubic.  We include in an extended Appendix selected Mathematica code which can beused to verify our computations independently.

Generalized Permutohedra, Scattering Amplitudes, and a Cubic Three-Fold