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math.AC2025
There is no polynomial formula for the catenary and the tame degree of finitely generated monoids
Alfred Geroldinger, Alessio Moscariello
In the last two decades there has been a wealth of results determining the precise value of the catenary degree and the tame degree. Mostly, however, only for very special classes…
math.AC2025
An upper bound for the multiplicity and Wilf's conjecture for one-dimensional Cohen-Macaulay rings
Marco D'Anna, Alessio Moscariello
In this work we provide an upper bound for the multiplicity of a one-dimensional Cohen-Macaulay ring (under certain conditions), describe the rings attaining the equality for this…
math.AC2025
Nearly Gorenstein numerical semigroups with five generators have bounded type
Alessio Moscariello, Francesco Strazzanti
We prove that the type of nearly Gorenstein numerical semigroups minimally generated by integers is bounded. In particular, if such a semigroup is not almost symmetric, then it…