Browsing by Author "Karakas, Halil Ibrahim"

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    Arf numerical semigroups
    (2017) Karakas, Halil Ibrahim; Ilhan, Sedat; AAY-4394-2021
    The aim of this work is to exhibit the relationship between the Arf closure of a numerical semigroup S and its Lipman semigroup L(S). This relationship is then used to give direct proofs of some characterizations of Arf numerical semigroups through their Lipman sequences of semigroups. We also give an algorithmic construction of the Arf closure of a numerical semigroup via its Lipman sequence of semigroups.
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    Arf numerical semigroups with multiplicity 11 and 13
    (2022) Karakas, Halil Ibrahim; Ilhan, Sedat; Suer, Meral; AAY-4394-2021
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    Arf Numerical Semigroups With Prime Multiplicity
    (2022) Karakas, Halil Ibrahim; AAY-4394-2021
    In the literature, parametrizations are given for Arf numerical semigroups with small multiplicity and arbitrary conductor. From those parametrizations, formulas are obtained for the number of such Arf numerical semigroups. These formulas show that the number of Arf numerical semigroups with multiplicity 3, 5 or 7 and arbitrary conductor depends only on the congruence class of the conductor modulo the multiplicity. In a recent work with S. Ilhan and M. Suer, observing that the same is true for Arf numerical semigroups with multiplicity 11 and 13, we asked if that was true for Arf numerical semigroups with arbitrary prime multiplicity. In the present work this question is answered affirmatively.
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    A decomposition of partitions and numerical sets
    (2020) Karakas, Halil Ibrahim; Tutas, Nesrin; C-2807-2016
    The aim of this work is to exhibit a decomposition of partitions of natural numbers and numerical sets. In particular, we obtain a decomposition of a sparse numerical set into the so called hook semigroups which turn out to be primitive. Since each Arf semigroup is sparse, we thus obtain a decomposition of any Arf semigroup into primitive numerical semigroups.