We discuss a particular problem of enumerating rational curves on a Grassmannian from several perspectives, including systems theory, real enumerative geometry, and symbolic computation. We also present a new transversality result, showing this problem is enumerative in all characteristics. While it is well-known how this enumerative problem arose in mathematical physics and also its importance...

In 2006, Espinola and Kirk made a useful contribution on combining fixed point theoryand graph theory. Recently, Reich and Zaslavski studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In this paper, by using  the main idea of their work and the idea of combining fixed point theory on intuitionistic fuzzy metric spaces and graph theory, ...

Dynamic detection and elimination of symmetry in constraints, is in general a hard task, but in Not-Equals binary constraint networks, the symmetry conditions can be simplified. In this paper, we extend the principle of symmetry to dominance in Not-Equals Constraint Networks and show how dominated values are detected and eliminated at each node of the search tree. A Linear time complexity algor...

The forcing polynomial and anti-forcing are two important enumerative polynomials associated with all perfect matchings of a graph. In graph large order, the exhaustive enumeration which is used to compute number given matching too time-consuming number. this paper, we come up an efficient method — integer linear programming, matching. As applications, obtain di-forcing C60 , C70 C72 as consequ...

Let d = (d1, d2, . . . , dn) be a vector of non-negative integers with even sum. We prove some basic facts about the structure of a random graph with degree sequence d, including the probability of a given subgraph or induced subgraph. Although there are many results of this kind, they are restricted to the sparse case with only a few exceptions. Our focus is instead on the case where the avera...

The Schubert Calculus is a formal calculus of symbols representing geometric conditions used to solve problems in enumerative geometry. This originated in work of Chasles [9] on conics and was systematized and used to great effect by Schubert in his treatise “Kalkül der abzählenden Geometrie” [33]. The justification of Schubert’s enumerative calculus and the verification of the numbers he obtai...

A stable (or independent) set in a graph is a set of pairwise non-adjacent vertices. The stability number α(G) is the size of a maximum stable set in the graph G. There are three different kinds of structures that one can see observing behavior of stable sets of a graph: the enumerative structure, the intersection structure, and the exchange structure. The independence polynomial of G