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The Frobenius Coin Problem—A Cylindrical Approach

  • Richard EhrenborgEmail author
Note
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Let a and b be two relatively prime positive integers, both greater than 1. Frobenius asked which values we can obtain using coins of denominations a and b. Since the sequence \(0, b, 2b, \ldots, (a-1) \cdot b\)

Notes

Acknowledgments

The author thanks Theodore Ehrenborg for comments on an earlier draft of this note. The author also thanks the Institute for Advanced Study for hosting a research visit in summer 2019, where this work was completed. This work was partially supported by a grant from the Simons Foundation (#429370 to Richard Ehrenborg).

References

  1. 1.
    E. Clark and R. Ehrenborg. The Frobenius complex. Ann. Comb. 16 (2012), 215–232.MathSciNetCrossRefGoogle Scholar
  2. 2.
    J. J. Sylvester. On subvariants, i.e. semi-invariants to binary quantics of an unlimited order. Amer. J. Math. 5 (1882), 79–136.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KentuckyLexingtonUSA

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