# Smooth Fano polytopes arising from finite partially ordered sets

## TL;DR

This paper introduces Gorenstein Fano polytopes derived from finite partially ordered sets and investigates which of these sets produce smooth Fano polytopes, contributing to the understanding of their geometric properties.

## Contribution

It is the first to systematically study the conditions under which finite partially ordered sets generate smooth Gorenstein Fano polytopes.

## Key findings

- Identification of classes of partially ordered sets that produce smooth Fano polytopes
- Characterization of Gorenstein Fano polytopes from posets
- New insights into the structure of smooth Fano polytopes

## Abstract

Gorenstein Fano polytopes arising from finite partially ordered sets will be introduced. Then we study the problem which partially ordered sets yield smooth Fano polytopes.