A formula for the number of (n-2)-gap in digital n-objects

TL;DR

This paper introduces a formula to calculate the number of (n-2)-gaps in digital n-objects using intrinsic parameters, facilitating automatic computation and analysis of cell bounding relationships.

Contribution

It provides a new combinatorial formula involving only simple intrinsic parameters, advancing the understanding of digital n-object structures.

Findings

Formula for (n-2)-gaps involving intrinsic parameters

Expressions for maximum number of i-cells bounding j-cells

Suitable for automatic computation models

Abstract

We provide a formula that expresses the number of (n-2)-gaps of a generic digital n-object. Such a formula has the advantage to involve only a few simple intrinsic parameters of the object and it is obtained by using a combinatorial technic based on incidence structure and on the notion of free cells. This approach seems suitable as a model for an automatic computation, and also allow us to find some expressions for the maximum number of i-cells that bound or are bounded by a fixed j-cell.