A recursive approach for the enumeration of the homomorphisms from a poset $P$ to the chain $C_3$

Abstract

Let $\mathcal{H}(P,C_3)$ be the set of order homomorphisms from a poset $P$ to the chain $C_3=1<2<3$. We develop a recursive approach for the calculation of the cardinality of $\mathcal{H}(P,C_3)$, and we apply it on several types of posets, including $P=C_3\times C_3\times C_k$ and $P=\mathcal{H}(C_k,C_3)$; for the latter poset $P$, we derive a direct formula for $\#\mathcal{H}(P,C_3)$.

25 pages, 10 figures