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The Corner Element of Generalized Numerical Semigroups

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Abstract

In this paper we introduce the concept of corner element of a generalized numerical semigroup, which extends in a sense the idea of conductor of a numerical semigroup to generalized numerical semigroups in higher dimensions. We present properties of this new notion and its relations with existing invariants in the literature, and provide an algorithm to compute all the generalized numerical semigroups with fixed corner. Besides that, we provide lower and upper bounds on the number of generalized numerical semigroups having a fixed corner element.

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Acknowledgements

The authors wish to thank the anonymous referee for her/his careful reading and valuable comments that helped to improve the previous version of this work.

Funding

The third author was supported by CNPq and FAPEMIG (grant numbers 307037/2019-3 and APQ-01661-17, respectively). The authors have no relevant financial or non-financial interests to disclose. All authors contributed to the study conception and design.

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Authors and Affiliations

  1. Faculdade do Gama, Universidade de Brasília, Brasília, DF, Brazil

    Matheus Bernardini

  2. Instituto de Ciências Exatas e da Terra, Universidade Federal de Mato Grosso, Cuiabá, MT, Brazil

    Wanderson Tenório

  3. Faculdade de Matemática, Universidade Federal de Uberlândia, Uberlândia, MG, Brazil

    Guilherme Tizziotti

Authors
  1. Matheus Bernardini
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  2. Wanderson Tenório
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  3. Guilherme Tizziotti
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Correspondence to Matheus Bernardini.

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Bernardini, M., Tenório, W. & Tizziotti, G. The Corner Element of Generalized Numerical Semigroups. Results Math 77, 141 (2022). https://doi.org/10.1007/s00025-022-01682-9

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  • DOI: https://doi.org/10.1007/s00025-022-01682-9

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