Lattice Partitions with a Straight Line

Abstract

In [1], the solution of a problem of distinct digital filter enumeration was expressed in terms of enumerating partitions of a rectangular set of lattice points with a straight line, under certain restrictions. Here, firstly, an explicit expression is derived for the number of such partitions in that and a more general case. Secondly, the asymptotic ratio of partitions to square of lattice dimensions is derived for a square lattice.