Minimal non-face of the triangulations

TL;DR

This paper investigates the minimal non-faces of triangulations of the standard unit d-cube, demonstrating shellability and calculating the h-polynomial, thereby advancing understanding of their combinatorial structure.

Contribution

It introduces the concept of minimal non-faces in triangulations of the d-cube and proves shellability along with deriving the h-polynomial for these triangulations.

Findings

Triangulations of the d-cube are shellable.

Explicit calculation of the h-polynomial for these triangulations.

Identification of minimal non-faces in the triangulations.

Abstract

In this paper, we discuss about the minimal non-faces of the triangulations $\Delta^d$ by the path of the standard unit $d$-cube. Moreover, we will show that $\Delta^d$ is shellable and the result of the calculation for $h$-polynomial of $\Delta^d$.