Two properties of maximal antichains in strict chain product posets

Shen-Fu Tsai

doi:10.11575/cdm.v15i3.62663

paper

Two properties of maximal antichains in strict chain product posets

arXiv:1701.06750 · doi:10.11575/cdm.v15i3.62663

Abstract

We present two results on maximal antichains in the strict chain product poset $[t_{1} + 1] \times [t_{2} + 1] \times \dots \times [t_{n} + 1]$ . 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 $[t_{1} + 1] \times [t_{2} + 1] \times \dots \times [t_{n} + 1]$ and antichains in the non-strict chain product poset $[t_{1}] \times [t_{2}] \times \dots \times [t_{n}]$ .