We give a complete classification of the factorial functions of Eulerian binomial posets. The factorial function B(n) either coincides with n!, the factorial function of the infinite Boolean algebra, or 2n−1, the factorial function of the infinite butterfly poset. We also classify the factorial functions for Eulerian Sheffer posets. An Eulerian Sheffer poset with binomial factorial function B(n...

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...

In this study, an Eulerian-Eulerian multi-fluid model (MFM) was used to simulate the segregation pattern of a conical fluidized bed containing ternary mixtures of equidensity TiO2‌ particles. Experimental 'freeze–sieving' method was employed to determine the axial mass fraction profiles of the different-sized particles, and validate the simulation results. The profiles of mass fraction for larg...

Here presented is the interrelationship between Eulerian polynomials, Eulerian fractions and Euler-Frobenius polynomials, Euler-Frobenius fractions, Bsplines, respectively. The properties of Eulerian polynomials and Eulerian fractions and their applications in B-spline interpolation and evaluation of Riemann zeta function values at odd integers are given. The relation between Eulerian numbers a...

We defined the symmetric TSP in lecture 6. The best known approximation algorithm for STSP is the 3/2 approximation algorithm of Christofides. The algorithm is very easy to describe, first choose a minimum cost spanning tree and then add that minimum cost Eulerian augmentation to the tree, that is the minimum cost set of edges to make the tree Eulerian. An undirected graph is Eulerian when ever...

Eulerian extension problems aim at making a given (directed) (multi-)graph Eulerian by adding a minimum-cost set of edges (arcs). These problems have natural applications in scheduling and routing and are closely related to the Chinese Postman and Rural Postman problems. Our main result is to show that the NP-hard Weighted Multigraph Eulerian Extension is fixed-parameter tractable with respect ...