82 research outputs found
Betti numbers for numerical semigroup rings
We survey results related to the magnitude of the Betti numbers of numerical
semigroup rings and of their tangent cones.Comment: 22 pages; v2: updated references. To appear in Multigraded Algebra
and Applications (V. Ene, E. Miller Eds.
Graver bases of shifted numerical semigroups with 3 generators
A numerical semigroup is a subset of the non-negative integers that is
closed under addition. A factorization of is an expression of as
a sum of generators of , and the Graver basis of is a collection
of trades between the generators of that allows for efficient
movement between factorizations. Given positive integers ,
consider the family of
"shifted" numerical semigroups whose generators are obtained by translating
by an integer parameter . In this paper, we characterize
the Graver basis of for sufficiently large in the case , in the form of a recursive construction of from that of smaller
values of . As a consequence of our result, the number of trades in
, when viewed as a function of , is eventually quasilinear. We also
obtain a sharp lower bound on the start of quasilinear behavior
- …