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arXiv · 1501.04523

Letterplace and co-letterplace ideals of posets

Gunnar Fløystad·Bjørn Møller Greve·Jürgen Herzog
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Abstract

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.

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Gunnar Fløystad, Bjørn Møller Greve, Jürgen Herzog. 2015-01-19. Letterplace and co-letterplace ideals of posets. https://doi.org/10.1016/j.jpaa.2016.09.007

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