In this article, we generalize the concepts of Eulerian and Hamiltonian digraphs to directed hypergraphs. A dihypergraph H is a pair (V(H), E(H)), where V(H) is a non-empty set of elements, called vertices, and E(H) is a collection of ordered pairs of subsets of V(H), called hyperarcs. It is Eulerian (resp. Hamiltonian) if there is a dicycle containing each hyperarc (resp. each vertex) exactly ...

Fabrication of an integrated circuit with smaller area, besides reducing the cost of manufacturing, usually causes a reduction in the power dissipation and propagation delay. Using the static CMOS technology to fabricate a circuit that realizes a specific logic function and occupies a minimum space, it must be implemented with continuous diffusion runs. Therefore, at the design stage, an Euleri...

Fabrication of an integrated circuit with smaller area, besides reducing the cost of manufacturing, usually causes a reduction in the power dissipation and propagation delay. Using the static CMOS technology to fabricate a circuit that realizes a specific logic function and occupies a minimum space, it must be implemented with continuous diffusion runs. Therefore, at the design stage, an Euleri...

In this paper we consider mixed volumes of combinations of hypersimplices. These numbers, called “mixed Eulerian numbers”, were first considered by A. Postnikov and were shown to satisfy many properties related to Eulerian numbers, Catalan numbers, binomial coefficients, etc. We give a general combinatorial interpretation for mixed Eulerian numbers and prove the above properties combinatorially...

A number of researchers studying permutation statistics on the symmetric group Sn have considered pairs (x, Y), where x is an Eulerian statistic and Y is a Mahonian statistic. Of special interest are pairs such as (des, maj), whose joint distribution on Sn is given by Carlitz’s q-Eulerian polynomials. We present a natural Eulerian statistic stc such that the pair (stc, inv) is equally distribut...

An undirected graph is Eulerian if it is connected and all its vertices are of even degree. Similarly, a directed graph is Eulerian, if for each vertex its in-degree is equal to its out-degree. It is well known that Eulerian graphs can be recognized in polynomial time while the problems of finding a maximum Eulerian subgraph or a maximum induced Eulerian subgraph are NP-hard. In this paper, we ...

Consider an undirected Eulerian graph, a graph in which each vertex has even degree. An Eulerian orientation of the graph is an orientation of its edges such that for each vertex v, the number of incoming edges of v equals to outgoing edges of v, i.e. din(v) = dout(v). Let P0 denote the set of all Eulerian orientations of graph G. In this paper, we are concerned with the questions of sampling u...

The aim of this study was to investigate the particulate dispersion from Kerman Cement Plant. The upwind – downwind method was used to measure particle concentration and a cascade impactor was applied to determine particle size distribution. An Eulerian model, Gaussian plume model and an artificial neural network have been used to compute and predict concentration of PM10 from Ke...