# Directed Plateau Polyhypercubes

## TL;DR

This paper investigates directed plateau polyhypercubes in dimensions three and higher, providing explicit formulas and generating functions based on width and a new lateral area parameter.

## Contribution

It introduces the concept of lateral area for directed plateau polyhypercubes and derives explicit formulas and generating functions for their enumeration.

## Key findings

- Explicit formula for counting directed plateau polyhypercubes
- Generating function expression based on width and lateral area
- Extension of polyhypercube enumeration to higher dimensions

## Abstract

In this paper, we study a particular family of polyhypercubes in dimension $d\geq 3$, the directed plateau polyhypercubes, according to to the width and a new parameter the lateral area. We give an explicit formula and we also propose an expression of the generating function in this case.