From spherical separation center set to the upper and lower bound theorems

TL;DR

This paper establishes upper and lower bounds on the sum of spherical face-partition pairs for simple spherical polytopes with a given number of facets, advancing understanding of spherical polytope combinatorics.

Contribution

It introduces new bounds for face-partition pairs in simple spherical polytopes, extending theoretical knowledge in spherical geometry.

Findings

Derived upper bounds for face-partition pairs.

Established lower bounds for face-partition pairs.

Enhanced theoretical framework for spherical polytope analysis.

Abstract

In this paper, we provide the upper bound and the lower bound of the sum of the number of spherical face-partition pair of simple spherical polytope $P$ with $p$ facets.