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...

The transport of fluid, heat ,and particles (bubbles and solid inclusions) in flowing molten steel is investigated in steel refining ladles, the continuous casting tundish, continuous casting mold and strand, and steel ingot casting processes. The two-equation k-ε model is used to simulate the turbulence. Multiphase fluid flow is numerically simulated with a Lagrangian-Eulerian approach, an Eul...

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...

We develop techniques that can be applied to find solutions to the recurrence ∣∣n k ∣∣ = ( n+ k + )∣∣n−1 k ∣∣+ ( ′n+ ′k + ′)∣∣n−1 k−1∣∣+ [n = k = 0]. Many interesting combinatorial numbers, such as binomial coefficients, both kinds of Stirling and associated Stirling numbers, Lah numbers, Eulerian numbers, and second-order Eulerian numbers, satisfy special cases of this recurrence. Our techniqu...

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...