# Ramsey theorem for designs

## TL;DR

This paper proves that all finite ordered designs with given parameters form a Ramsey class, extending the understanding of combinatorial structures in Ramsey theory.

## Contribution

It establishes the Ramsey property for the class of all finite ordered designs with arbitrary parameters $k,t, ext{and}\,\lambda$.

## Key findings

- Finite ordered designs with parameters $k,t, ext{and}\, ext\,\\lambda$ form a Ramsey class.
- The result generalizes previous Ramsey theorems to a broad class of combinatorial designs.
- Provides a new framework for analyzing ordered combinatorial structures in Ramsey theory.

## Abstract

We prove that for any choice of parameters $k,t,\lambda$ the class of all finite ordered designs with parameters $k,t,\lambda$ is a Ramsey class.