Based Based on on two two inversion inversion formulas formulas for for enumerating enumerating words words in in the the free free monoid monoid by by adjacencies, adjacencies, we we present present a a new new approach approach to to a a class class of of permutation permutation problems problems having having Eulerian-type Eulerian-type generating generating functions. functions. We We also ...

A poset P is called k-Eulerian if every interval of rank k is Eulerian. The class of k-Eulerian posets interpolates between graded posets and Eulerian posets. It is a straightforward observation that a 2k-Eulerian poset is also (2k+1)-Eulerian. We prove that the ab-index of a (2k+1)Eulerian poset can be expressed in terms of c = a + b, d = ab + ba and e2k+1 = (a − b)2k+1. The proof relies upon ...

Eulerian poset is a basic and widely used combinatorial concept. It is the combinatorial version of manifolds and has the analogue of the Poincaré duality in the form of the DehnSommerville equations (linear relations among f -vectors). The concept has always been defined in the combinatorial language. As a topologist, my main insight is that a poset is Eulerian if and only if its underlying po...

A novel 3D computational model was developed for the turbulent particulate two-phase flow simulation in rectangular channel. The is based on Eulerian approach applied to Reynolds-averaged Navier–Stokes modeling and statistical Probability Distribution Function method. uniqueness of method lies direct calculation normal transverse components Reynolds stresses both gas particles. Two cases were e...

A Large Eddy Simulation approach for Eulerian-Eulerian dispersed two-phase flow is presented. It is shown that not only a Sub-Grid Scales term modeling the unresolved field in the mesoscopic momentum transport equation of the dispersed phase, but also a stress term modeling the Random-Uncorrelated Motion is needed. Simulations of a non-homogeneous particle laden turbulent gas flow allow to comp...

Formation of a dispersed oil—water flow pattern is common occurrence in lines and pipelines. The capability predicting the size droplets, as well distribution phase volume fraction utmost importance for proper design such systems. present study aims at modelling water oil flows horizontal pipe by employing multi-fluid Eulerian approach along with population balance model. To this end, momentum ...

In this paper, we evaluate the number of Eulerian circuits that can be obtained by an arbitrary rotation in a Markovian string, i.e., corresponding to a given Markovian type. Since all rotations do not result in an Eulerian circuit, but several of them, called Eulerian components; we also investigate the number of Eulerian components that result from a random rotation in a Markovian string. We ...