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On Sylvester sums of compound sequence semigroup complements.

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Title: On Sylvester sums of compound sequence semigroup complements.
Authors: Gassert, T. Alden1 thomas.gassert@wne.edu, Shor, Caleb McKinley1 cshor@wne.edu
Source: Journal of Number Theory. Nov2017, Vol. 180, p45-72. 28p.
Subjects: Natural numbers, Weierstrass-Stone theorem, Algebraic equations, Sylvester matrix equations, Integers
Abstract: In this paper, we consider the set NR ( G ) of natural numbers which are not in the numerical semigroup generated by a compound sequence G . We generalize a result of Tuenter which completely characterizes NR ( G ) . We use this result to compute Sylvester sums, and we give a direct application to the computation of weights of higher-order Weierstrass points on some families of complex algebraic curves. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: On Sylvester sums of compound sequence semigroup complements.
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  Data: In this paper, we consider the set NR ( G ) of natural numbers which are not in the numerical semigroup generated by a compound sequence G . We generalize a result of Tuenter which completely characterizes NR ( G ) . We use this result to compute Sylvester sums, and we give a direct application to the computation of weights of higher-order Weierstrass points on some families of complex algebraic curves. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.jnt.2017.03.025
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      – Code: eng
        Text: English
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        PageCount: 28
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      – SubjectFull: Natural numbers
        Type: general
      – SubjectFull: Weierstrass-Stone theorem
        Type: general
      – SubjectFull: Algebraic equations
        Type: general
      – SubjectFull: Sylvester matrix equations
        Type: general
      – SubjectFull: Integers
        Type: general
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      – TitleFull: On Sylvester sums of compound sequence semigroup complements.
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              Text: Nov2017
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