We introduce a new basis for the polynomial ring which has its genesis in the computation of the cohomology class of the permutahedral variety. We will see that this basis is very well-behaved in regards to reduction modulo the ideal of quasisymmetric polynomials. This has interesting ramifications of a discrete-geometric flavour that we will discuss -- for instance, a multivariate analogue of mixed Eulerian numbers comes up naturally, amongst other things.

Joint with Philippe Nadeau (CNRS and Univ. Lyon).