1995
DOI: 10.1016/0022-4049(94)00058-q
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On the Hilbert function of certain rings of monomial curves

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Cited by 24 publications
(18 citation statements)
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“…Note that since the explicit description of the standard basis of the numerical semigroup Γ generated by an almost arithmetic progression in known (for example, see [17,18]), one can use the above theorem to obtain the proofs of the results proved in [13,12] much easily than their original proofs.…”
Section: Lemma 13mentioning
confidence: 97%
See 3 more Smart Citations
“…Note that since the explicit description of the standard basis of the numerical semigroup Γ generated by an almost arithmetic progression in known (for example, see [17,18]), one can use the above theorem to obtain the proofs of the results proved in [13,12] much easily than their original proofs.…”
Section: Lemma 13mentioning
confidence: 97%
“…This proves once again 1.1(3) for a semigroup ring R: The degree deg(h R ) of the h-polynomial is the reduction exponent r 0 , of R. Further, if G(Γ ) is Cohen-Macaulay, then h R (Z) = ∑ r 0 r=0 |S(r)| · Z r by Theorem 1.6 and 1.9(3). If Γ is generated by an arithmetic progression, then G(Γ ) is always Cohen-Macaulay and the explicit computation of the hpolynomial is done in [13]. If Γ is generated by an almost arithmetic progression, then a characterization for the CohenMacaulayness of G(Γ ) is given (in most cases) in [12] and the explicit computation of the h-polynomial is done in [20].…”
Section: Lemma 13mentioning
confidence: 99%
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“…We recall that G is Cohen-Macaulay (Proposition 1.1 in [11]) and, if a 0 = (t − 1)n + r, t ≥ 2 and 1 ≤ r ≤ n, then the h-polynomial of G is…”
Section: Preliminariesmentioning
confidence: 99%