3 papers
math.AC2024
On the ordinary and symbolic powers of fiber products
Hoang Viet Do, Hop D. Nguyen, Seyed Amin Seyed Fakhari
We completely determine the depth and regularity of symbolic powers of the fiber product of two homogeneous ideals in disjoint sets of variables, given knowledge of the symbolic po…
math.AC2024
Unboundedness of irreducible decompositions of numerical semigroups
Tristram Bogart, Seyed Amin Seyed Fakhari
We present two families of numerical semigroups and show that for each family, the number of required components in an irreducible decomposition cannot be bounded by any given inte…
math.AC2024
Some inequalities regarding the regularity of powers of monomial ideals
S. A. Seyed Fakhari
We prove some inequalities regarding the Castelnuovo--Mumford regularity of symbolic powers and integral closure of powers of monomial ideals.