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Frobenius numbers of numerical semigroups generated by three consecutive squares or cubes

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Abstract

We establish and prove polynomial formulas for the Frobenius numbers of numerical semigroups generated by \(n^2, (n+1)^2, (n+2)^2\) and by \(n^3, (n+1)^3, (n+2)^3\). The formulas depend on the residue class of \(n\) modulo 4 and 18, respectively.

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Authors and Affiliations

  1. Department of Mathematics, Reed College, 3203 SE Woodstock Blvd., Portland, OR, 87202, USA

    Mikhail Lepilov & Irena Swanson

  2. Department of Philosophy, Princeton University, Princeton, NJ, 08544, USA

    Joshua O’Rourke

Authors
  1. Mikhail Lepilov
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  2. Joshua O’Rourke
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  3. Irena Swanson
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Corresponding author

Correspondence to Irena Swanson.

Additional information

Communicated by Fernando Torres.

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Lepilov, M., O’Rourke, J. & Swanson, I. Frobenius numbers of numerical semigroups generated by three consecutive squares or cubes. Semigroup Forum 91, 238–259 (2015). https://doi.org/10.1007/s00233-014-9687-8

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  • DOI: https://doi.org/10.1007/s00233-014-9687-8

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