# Two properties of maximal antichains in strict chain product posets

## TL;DR

This paper investigates properties of maximal antichains in strict chain product posets, proving they are also maximum and establishing a bijection with antichains in non-strict chain product posets, thus advancing combinatorial understanding.

## Contribution

It demonstrates that maximal antichains in strict chain product posets are also maximum and establishes a bijection with antichains in non-strict chain product posets.

## Key findings

- Maximal antichains are also maximum in strict chain product posets.
- A bijection exists between maximal antichains in strict and antichains in non-strict chain product posets.

## Abstract

We present two results on maximal antichains in the strict chain product poset $[t_1+1]\times[t_2+1]\times\ldots\times[t_n+1]$. First, we prove that these maximal antichains are also maximum. Second, we prove that there is a bijection between maximal antichains in the strict chain product poset $[t_1+1]\times[t_2+1]\times\ldots\times[t_n+1]$ and antichains in the non-strict chain product poset $[t_1]\times[t_2]\times\ldots\times[t_n]$.