A Koszul filtration for the third squarefree Veronese subring

Abstract We show the existence of a Koszul filtration for the third squarefree Veronese subring. A Koszul filtration is a generalization of the concept of a Koszul algebra and consists of a family of ideals generated by linear forms satisfying specific properties. We introduce a new concept of ridge chordality for 3-uniform hypergraphs, which captures a suitable structure to construct a Koszul filtration, using this new combinatorial tool. This approach bridges the gap between combinatorial properties of hypergraphs and algebraic structures, contributing to a deeper understanding of squarefree Veronese rings.