A pair correlation problem, and counting lattice points with the zeta function

Pair Correlation Function Realizability: Lattice Model Implications†

Despite their long history in experiment, simulation, and analytical theory, pair correlation functions that describe local order in many-body systems still retain a legacy of mathematical mysteries. One such open question concerns “realizability” of a given candidate pair correlation function, namely whether it actually represents the pair correlation for some spatial distribution of particles...

Counting Lattice Points in Polyhedra

We present Barvinok’s 1994 and 1999 algorithms for counting lattice points in polyhedra. 1. The 1994 algorithm In [2], Barvinok presents an algorithm that, for a fixed dimension d, calculates the number of integer points in a rational polyhedron. It is shown in [6] and [7] that the question can be reduced to counting the number of integer points in a k-dimensional simplex with integer vertices ...

Visible Lattice Points and the Chromatic Zeta Function of a Graph

We study the probability that a random polygon of k vertices in the lattice {1, . . . , n}s does not contain more lattice points than the k vertices of the polygon. Then we introduce the chromatic zeta function of a graph to generalize this problem to other configurations induced by a given graph H.

Counting Function Points for

Function points (FPs) are proven to be effective and efficient units of measure for both agile/iterative and waterfall software deliveries. However, inconsistencies come to light when comparing FPs counted in agile/iterative development with those counted in waterfall or combination development – and those inconsistencies can create confusion for cost, productivity, and schedule evaluations tha...

Pair-correlation function in 2-dimensional lattice gases