Two properties of maximal antichains in strict chain product posets

Abstract

We present two results on maximal antichains in the strict chain product poset $[t_1+1]\times[t_2+1]\times\cdots\times[t_n+1]$. 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 $[t_1+1]\times[t_2+1]\times\cdots\times[t_n+1]$ and antichains in the nonstrict chain product poset $[t_1]\times[t_2]\times\cdots\times[t_n]$.

Published
2020-12-22
Section
Articles