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...

Granular flow simulation using CFD has received a lot of attention in recent years. In such cases, CFD is either, coupled with Discrete Element Method (DEM) techniques for appropriate incorporation of inter-particle collisions, or the Eulerian CFD approach is used in which granular particles are treated as they were fluid. In the present study, a CFD analysis was performed...

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...

In this paper, we give a combinatorial interpretation of the r-Whitney-Eulerian numbers by means of coloured signed permutations. This sequence is a generalization of the well-known Eulerian numbers and it is connected to r-Whitney numbers of the second kind. Using generating functions, we provide some combinatorial identities and the log-concavity property. Finally, we show some basic congruen...

We prove two conjectures of Shareshian and Wachs about Eulerian quasisymmetric functions and polynomials. The first states that the cycle type Eulerian quasisymmetric function Qλ,j is Schur-positive, and moreover that the sequence Qλ,j as j varies is Schur-unimodal. The second conjecture, which we prove using the first, states that the cycle type (q, p)-Eulerian polynomial A λ (q, p, q −1t) is ...