We investigate the Castelnuovo–Mumford regularity and the multiplicity of the toric ring associated with a three-dimensional Ferrers diagram. In particular, in the rectangular case, we provide direct formulas for these two important invariants. Then, we compare these invariants for an accompanying pair of Ferrers diagrams under some mild conditions and bound the Castelnuovo–Mumford regularity for more general cases.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics