3 papers
math.AC2025
Scarf complexes of connected and path ideals
Trung Chau, Richie Sheng, Tim Tribone +1
The -connected ideal of a graph is generated by all connected induced subgraphs of with vertices. When , this coincides with the usual edge ideal of the graph…
math.AC2025
Tensor products of -fold matrix factorizations
Richie Sheng, Tim Tribone
Consider a pair of elements and in a commutative ring . Given a matrix factorization of and another of , the tensor product of matrix factorizations, which was fi…
math.AC2025
Homological invariants of edge ideals of weighted oriented graphs
Trung Chau, Richie Sheng, Deborah Wooton
We determine all possible triples of depth, dimension, and regularity of edge ideals of weighted oriented graphs with a fixed number of vertices. Also, we compute all the possible…