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 succe...

Kim et al. 2012 introduced an interesting p-adic analogue of the Eulerian polynomials. They studied some identities on the Eulerian polynomials in connection with the Genocchi, Euler, and tangent numbers. In this paper, by applying the symmetry of the fermionic p-adic q-integral on Zp, defined by Kim 2008 , we show a symmetric relation between the q-extension of the alternating sum of integer p...

Let G be an Eulerian directed graph with an arc-labeling such that arcs going out from the same vertex have di erent labels. In this work, we present an algorithm to construct the Eulerian trail starting at an arbitrary vertex v of minimum lexicographical label among labels of all Eulerian trails starting at this vertex. We also show an application of this algorithm to construct the minimal de ...

In [13], we introduced the notion of Eulerian stratified spaces. In this paper, we study in detail the topological and combinatorial properties of Eulerian 2strata spaces, as the first step toward a deeper understanding of more strata cases. We show that Eulerian 2-strata spaces have similar topological structure as topological 2-strata spaces. Moreover, we find all the linear conditions on f -...

In this paper we describe routing functions for optical packets in point-to-point networks. These functions are based on Eulerian tours. We first define different measures to handle the efficiency of this routing. Then, we describe an algorithm to compute these measures. Moreover, we present such an Eulerian routing in the Square Mesh and we prove that the induced paths are close to the optimal...

We consider several generalizations of the classical γ-positivity of Eulerian polynomials using generating functions and combinatorial theory of continued fractions. For the symmetric group, we prove an expansion formula for inversions and excedances as well as a similar expansion for derangements. We also prove the γ-positivity for Eulerian polynomials of type B and for Eulerian polynomials of...

We introduce the notion of an Eulerian graph being strongly evencycle decomposable, and note that a few basic classes have this property. Our main results are that several fundamental composition operations that preserve the property of being Eulerian also preserve the property of being strongly even-cycle decomposable. As an application, our composition operations easily imply that all Euleria...

This work advocates Eulerian motion representation learning over the current standard Lagrangian optical flow model. Eulerian motion is well captured by using phase, as obtained by decomposing the image through a complexsteerable pyramid. We discuss the gain of Eulerian motion in a set of practical use cases: (i) action recognition, (ii) motion prediction in static images, (iii) motion transfer...