TELESCOPIC NUMERICAL SEMIGROUPS WITH MULTIPLICITY TEN AND EMBEDDING DIMENSION THREE

Öz

In this work, we give parametrizations of telescopic numerical semigroups with multiplicity ten and embedding dimension three. We also express some of its invariants in terms of generators of these semigroups such as the Frobenius number, genus and Sylvester number.

Anahtar Kelimeler

• Frobenius number
• genus
• Sylvester number
• Telescopic numerical semigroup

Kaynakça

1. V. Barucci, D. Dobbs and M. Fontana, Maximality Properties in Numerical Semigroups and Applications to One-Dimensional Analytically Irreducible Local Domains, Vol. 598, Memoirs of the American Mathematical Society, Providence, RI, (1997).
2. A. Brauer, On a problem of partitions. Amer. J. Math., 64, (1942), 299-312.
3. F. Curtis, On Formulas fort he Frobenius number of a numerical semigroup. Math Scand., 67, (1990), 190-192.
4. D.E. Dobbs and G.L.Matthews, On Comparing two chains of numerical semigroups and detecting Arf semigroups. Semigroups Forum, 63, (2001), 237-246.
5. R. Fr¨oberg, C. Gottlieb and R. H¨aggkvist, On numerical semigroups. Semigroup Forum, 35, (1987), 63–83.
6. J. Herzog, Generators and relations of abelian semigroup and semigroups rings. Manuscripta Math., 3, (1970), 175-193.
7. C. Hollings, A History of the Algebraic Theory of Semigroups, Vol. 41, American Mathematical Society Providence, Rhode Island, pp. 16-17 (2014).
8. S. ˙Ilhan, On a class of telescopic numerical semigroups. Int. J. Contemporary Math. Sci., 1(2), (2006), 81-83.

9. S. ˙Ilhan, Some results in a class of telescopic numerical semigroups. Al-Qadisiyah Journal of Pure Science, 25(4), (2020), 40-45.
10. S.M. Johnson, A linear Diophantine problem, Canad. J. Math., 12, (1960), 390-398.
11. C. Kirfeland and R. Pellikaan, The minimum distance of codes in an array coming telescopic semigroups. Special issue on algebraic geometry codes, IEEE Trans. Inform. Theory, 41, (1995), 1720-1732.
12. E. Kunz, The value semigroup of an one dimensional Gorenstein ring. Proc. Amer. Math.Soc., 25, (1970), 748-751.
13. J.C. Rosales and P.A. Garcia-S´anchez, Numerical semigroups, Vol. 181, Springer, New York, (2009).
14. J.C. Rosales and P.A. Garcia-S´anchez, On free affine semigroups. Semigroup Forum, 58(3), (1999), 367–385.
15. M. S¨uer and S. ˙Ilhan, All Telescopic Numerical Semigroups With Multiplicity Four and Six. Journal of Science and Technology, Erzincan Universty, 12(1), (2019), 457-462.
16. M. S¨uer and ˙Ilhan, On triply generated telescopic semigroups with multiplicity 8 and 9. Comptes rendus de l’Academie bulgare des Sciences, 72(3), (2020), 315-319.
17. J.J. Sylvester, Problem 7382, in W. J. C. Miller, ed., Mathematical Questions, with their Solutions. Educational Times, 41, (1884), 21.
18. K. Watanabe, Some examples of one dimensional Gorenstein domains. Nagoya Math. J., 49, (1973), 101–109.