Remixed Eulerian numbers

Abstract Remixed Eulerian numbers are a polynomial q -deformation of Postnikov’s mixed numbers. They arose naturally in previous work by the authors concerning permutahedral variety and subsume well-known families polynomials such as -binomial coefficients Garsia–Remmel’s -hit We study their combinatorics more depth. As , they shown to be symmetric unimodal. By interpreting them computing success probabilities simple probabilistic process we arrive at combinatorial interpretation involving weighted trees. decomposing permutahedron into certain cubes, obtain second interpretation. At $q=1$ former recovers whereas latter Liu’s interpretation, both which were obtained via methods different from ours.