On the relations of isotonian algebras

TL;DR

This paper investigates the algebraic structure of isotonian algebras, showing that for many poset classes, their defining ideals are generated by squarefree binomials, and classifying when these are quadratically generated.

Contribution

It characterizes classes of posets for which the defining ideals of isotonian algebras are generated by squarefree binomials and identifies when these ideals are quadratically generated.

Findings

Defining ideals are generated by squarefree binomials for large classes of posets.

Classification of posets with quadratically generated defining ideals.

Structural insights into the algebraic properties of isotonian algebras.

Abstract

It is shown that for large classes of posets $P$ and $Q$, the defining ideal $J_{P,Q}$ of an isotonian algebras is generated by squarefree binomials. Within these classes, those posets are classified for which $J_{P,Q}$ is quadratically generated.