The goal of this paper is to show that valuation theory and Hopf theory are compatible on the
class of generalized permutahedra. We prove that the Hopf structure on these polyhedra …

A bstract We present a general construction of two types of differential forms, based on any
(n− 3)-dimensional subspace in the kinematic space of n massless particles. The first type is …

The resonance arrangement A n is the arrangement of hyperplanes which has all non-zero
0/1-vectors in R n as normal vectors. It is the adjoint of the Braid arrangement and is also …

A bstract We present a new formula for the biadjoint scalar tree amplitudes m (α| β) based on
the combinatorics of dual associahedra. Our construction makes essential use of the cones …

Normal ordering in the eyl algebra is related to the Stirling numbers of the second kind,
while normal ordering in the shift algebra is related to the unsigned Stirling numbers of the …

On configuration spaces and Whitehouse's lifts of the Eulerian representations - ScienceDirect
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We study a certain discrete differentiation of piecewise-constant functions on the adjoint of
the braid hyperplane arrangement, defined by taking finite-differences across hyperplanes …

In this note, we study the permutohedral geometry of the poles of a certain differential form
introduced in recent work of Arkani-Hamed, Bai, He and Yan. There it was observed that the …

Alcoved polytopes are characterized by the property that all facet normal directions are
parallel to the roots $ e_i-e_j $. Unlike other prominent families of polytopes, like …

The commutative Hopf monoid of set compositions is a fundamental Hopf monoid internal to
vector species, having undecorated bosonic Fock space the combinatorial Hopf algebra of …