This paper is concerned with the counting and random sampling of plane graphs (simple planar graphs embedded in the plane). Our main result is a bijection between the class of plane graphs with triangular outer face, and a class of oriented binary trees. The number of edges and vertices of the plane graph can be tracked through the bijection. Consequently, we obtain counting formulas and an eff...

We introduce “rooted valuation products” and use them to construct universal Abelian lattice-ordered groups (with prescribed set of components) [CHH] from the more classical theory of [Ha]. The Wreath product construction of [H] and [HMc] generalised the Abelian (lattice-ordered) group ideas to a permutation group setting to respectively give universals for transitive (`-) permutation groups wi...

We examine some properties of the 2-variable greedoid polynomial f(G;t, z) when G is the branching greedoid associated to a rooted graph or a rooted directed graph. For rooted digraphs, we show a factoring property of f (G;t ,z) determines whether or not the rooted digraph has a directed cycle.

One of the recent inquiries in the field of hadith studies is the investigation of transferred traditions and their causes and impacts on Shi‘i hadith circles. By exploring some traditions in the hadith collection of al-Shaykh al-Saduq and comparing the textual similarities and also the chain of transmitters, this research attempts to show that traditions of Jewish origin in the Shi‘i hadith ci...

provided the original work is properly cited. CC Patients, especially pediatric patients, with a recent history of an upper respiratory tract infection (URI) are at a significantly increased risk for the development of intraoperative airway complications due to airway hyperreactivity. For these patients, the incidence for bronchospasm can be 10 times the incidence for those patients who did not...

The study of the cultural and aesthetic component advertising is aimed at determining significant influence ethno-artistic traditions Ukraine on stylistics graphics. authors consider problems national form reasons for pseudo-nationalization in design advertising. As a result color-graphic semantic analysis numerous works art, it was found that visual components graphics are deeply rooted Ukrain...

In this paper, we construct explicitly a NCS system ([Z4]) Ω T ∈ (H GL) ×5 over the Grossman-Larson Hopf algebra H GL ([GL] and [F]) of rooted trees labeled by elements of a nonempty W ⊆ N of positive integers. By the universal property of the NCS system (NSym,Π) formed by the generating functions of certain NCSF’s ([GKLLRT]), we obtain a graded Hopf algebra homomorphism TW : NSym → H GL such t...

the expansion of grey- black pottery tradition in the iranian plateau, on the basis of iron age theory of cultural dynamism, was emerged by the end of the 2nd millennium bc. such a pottery tradition is regarded as a cultural sign to point migrants who entered in the iranian plateau from the northern outside of caucasus the major. according to the theory, the migrants passed the river valley of ...