M^♮-convexity and ultramodularity on integer lattice

Integer Partitions and Convexity

Let n be an integer ≥ 1, and let p(n, k) and P (n, k) count the number of partitions of n into k parts, and the number of partitions of n into parts less than or equal to k, respectively. In this paper, we show that these functions are convex. The result includes the actual value of the constant of Bateman and Erdős.

A Mixed Integer Convexity Result with an Application to an M/M/s Queueing System

Many optimization problems in queueing theory have functions with integer and real variables. Convexity results for these functions can be obtained by fixing either the integer or the real variable where bounds of the considered function play an important role. Tokgöz, Maalouf and Kumin [11] introduces the concept of mixed convexity for functions with real and integer variables and obtain conve...

Integer Lattice

We generalize the hydrodynamic lattice gas model to include arbitrary numbers of particles moving in each lattice direction. For this generalization we derive the equilibrium distribution function and the hydrodynamic equations, including the equation of state and the prefactor of the inertial term that arises from the breaking of galilean invariance in these models. We show that this prefactor...

Integer Lattice Gases

We generalize the hydrodynamic lattice gas model to include arbitrary numbers of particles moving in each lattice direction. For this generalization we derive the equilibrium distribution function and the hydrodynamic equations, including the equation of state and the prefactor of the inertial term that arises from the breaking of galilean invariance in these models. We show that this prefactor...

On Cliques and Forcing m-Convexity Numbers of Graphs