2018
DOI: 10.1007/978-3-319-90493-1_8
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Betti Numbers for Numerical Semigroup Rings

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Cited by 20 publications
(17 citation statements)
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“…, n e + j } j≥0 seem to change periodically with j, for j ≫ 0. This goes in the same direction as a recent number of other results about eventually periodic properties in this shifted family, see [16], [32], [14], [30], [4], [24]. Using [29], we prove in Theorem 3.2 that given n 1 < n 2 < n 3 and letting H j = n 1 + j, n 2 + j, n 3 + j we have res(H j ) = res(H j+(n 3 −n 1 ) ) for all j ≫ 0.…”
Section: Introductionsupporting
confidence: 85%
“…, n e + j } j≥0 seem to change periodically with j, for j ≫ 0. This goes in the same direction as a recent number of other results about eventually periodic properties in this shifted family, see [16], [32], [14], [30], [4], [24]. Using [29], we prove in Theorem 3.2 that given n 1 < n 2 < n 3 and letting H j = n 1 + j, n 2 + j, n 3 + j we have res(H j ) = res(H j+(n 3 −n 1 ) ) for all j ≫ 0.…”
Section: Introductionsupporting
confidence: 85%
“…Here a 1 = 4, a 2 = 3, a 3 = 3, a 4 = 5, u 1 = 9, u 2 = 3, u 3 = 2 and u 4 = 7. Consider the vector v 1 = (9,12,15,9). For all w ≥ 0 the ideal I(n + wv 1 ) is a complete intersection on Theorem 2.8.…”
Section: Proof Consider the Vectors Dmentioning
confidence: 99%
“…Example 2.10. Let n = (15,25,24,16), then I(n) is a complete intersection on the binomials x 5 1 −x 3 2 , x 2 3 −x 3 4 and x 1 x 2 −x 3 x 4 . Here a 1 = 5, a 2 = 3, a 3 = 2, a 4 = 3, u i = 1, 1 ≤ i ≤ 4.…”
Section: Proof Consider the Vectors Dmentioning
confidence: 99%
See 1 more Smart Citation
“…We make repeated use of the following effective result as in [7,8,12] in order to reduce the number of cases for determining the Betti numbers of the tangent cones. Lemma 1.2.…”
mentioning
confidence: 99%