turkmath.org

Our main goal is to study the ideal L(P,Q) and toric ring K[P,Q] whose generators are in bijection to the isotone maps from P to Q. We examine the several algebraic properties of L(P,Q) including Alexander duality behavior. The class of algebras K[P,Q], called isotonian, are natural generalizations of the so-called Hibi rings. We determine the Krull dimension of these algebras and for particular classes of posets P and Q we show that K[P,Q] is normal and that their defining ideal admits a quadratic Grobner basis.