Mathematics Colloquia and Seminars
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On factorization invariants and Hilbert functionsAlgebra & Discrete Mathematics
Nonunique factorization in commutative monoids is often studied through the use of factorization invariants, which assign to each monoid element a quantity determined by the factorization structure. For numerical monoids (additive submonoids of the natural numbers), several factorization invariants are known to admit predictable behavior for sufficiently large elements. In particular, the catenary degree and delta set invariants are both eventually periodic, and the omega-primality invariant is eventually quasilinear. In this talk, we demonstrate how each of these invariants can be determined by Hilbert functions of graded modules. In doing so, we recover the aforementioned eventual behavior results for numerical monoids, as well as extend these results to pointed affine monoids.