Counting all, counting on, counting up, counting down

On Counting Polynomials of Some Nanostructures

The Omega polynomial(x) was recently proposed by Diudea, based on the length of strips in given graph G. The Sadhana polynomial has been defined to evaluate the Sadhana index of a molecular graph. The PI polynomial is another molecular descriptor. In this paper we compute these three polynomials for some infinite classes of nanostructures.

Curve Counting and Instanton Counting

Intuitively, in four-dimensional gauge theories one counts instantons, and in twodimensional string theory one counts holomorphic curves. These correspond to the instanton counting and curve counting in the title. There is no obvious connection between them, but a remarkable physical idea called geometric engineering [9, 10, 11] dictates that they are indeed related. More precisely, the generat...

Counting on

Counting All DCJ Sorting Scenarios

In genome rearrangements, the double cut and join (DCJ) operation, introduced by Yancopoulos et al., allows to represent most rearrangement events that could happen in multichromosomal genomes, such as inversions, translocations, fusions and fissions. No restriction on the genome structure considering linear and circular chromosomes is imposed. An advantage of this general model is that it lead...

On the Means of the Values of Prime Counting Function

In this paper, we investigate the means of the values of prime counting function $pi(x)$. First, we compute the arithmetic, the geometric, and the harmonic means of the values of this function, and then we study the limit value of the ratio of them.