To a natural number $n$, a finite partially ordered set $P$ and a poset ideal ${ \mathcal J}$ in the poset $Hom(P,[n])$ of isotonian maps from $P$ to the chain on $n$ elements, we associate two monomial ideals, the letterplace ideal $L(n,P;{ \mathcal J})$ and the co-letterplace ideal $L(P,n;{ \mathcal J})$. These ideals give a unified understanding of a number of ideals studied in monomial ideal theory in recent years. By cutting down these ideals by regular sequences of variable differences we obtain: multichain ideals and generalized Hibi type ideals, initial ideals of determinantal ideals, strongly stable ideals, $d$-partite $d$-uniform ideals, Ferrers ideals, edge ideals of cointerval $d$-hypergraphs, and uniform face ideals.
Categories: math.AC