# Binomial edge rings associated to skew Ferrers diagrams

## TL;DR

This paper studies binomial edge rings linked to skew Ferrers diagrams, constructing a quadratic Gröbner basis and proving properties like Koszulness, Cohen-Macaulayness, normality, and determining Krull dimension.

## Contribution

It introduces a new approach using Sagbi basis theory to analyze binomial edge rings associated with skew Ferrers diagrams, establishing their algebraic properties.

## Key findings

- Constructed a quadratic Gröbner basis for the ring's defining ideal
- Proved the ring is Koszul, Cohen-Macaulay, and a normal domain
- Determined the Krull dimension precisely

## Abstract

In this study, we investigate the binomial edge ring associated with the skew Ferrers diagram. By employing Sagbi basis theory, we construct a quadratic Gr\"{o}bner basis for its defining ideal. As an application, we prove that this ring is a Koszul, Cohen-Macaulay, normal domain. Moreover, we precisely determine its Krull dimension.