A generalization of Sylvester's and Frobenius' problems on numerical semigroups

Zdzisław Skupień

Acta Arithmetica (1993)

  • Volume: 65, Issue: 4, page 353-366
  • ISSN: 0065-1036

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Zdzisław Skupień. "A generalization of Sylvester's and Frobenius' problems on numerical semigroups." Acta Arithmetica 65.4 (1993): 353-366. <http://eudml.org/doc/206585>.

@article{ZdzisławSkupień1993,
author = {Zdzisław Skupień},
journal = {Acta Arithmetica},
keywords = {numerical semigroup; Frobenius problem; linear diophantine equation; integer sumsets; open problems; modular change problem; pseudo-polynomial algorithms; upper bound},
language = {eng},
number = {4},
pages = {353-366},
title = {A generalization of Sylvester's and Frobenius' problems on numerical semigroups},
url = {http://eudml.org/doc/206585},
volume = {65},
year = {1993},
}

TY - JOUR
AU - Zdzisław Skupień
TI - A generalization of Sylvester's and Frobenius' problems on numerical semigroups
JO - Acta Arithmetica
PY - 1993
VL - 65
IS - 4
SP - 353
EP - 366
LA - eng
KW - numerical semigroup; Frobenius problem; linear diophantine equation; integer sumsets; open problems; modular change problem; pseudo-polynomial algorithms; upper bound
UR - http://eudml.org/doc/206585
ER -

References

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  3. [3] P. Erdős and R. L. Graham, On a linear diophantine problem of Frobenius, Acta Arith. 21 (1972), 399-408. Zbl0246.10010
  4. [4] R. Fröberg, C. Gottlieb and R. Häggkvist, On numerical semigroups, Semigroup Forum 35 (1987), 63-83. Zbl0614.10046
  5. [5] S. Kertzner, The linear diophantine equation, Amer. Math. Monthly 88 (1981), 200-203. Zbl0458.10014
  6. [6] S. Morito and H. M. Salkin, Finding the general solution of a linear diophantine equation, Fibonacci Quart. 17 (1979), 361-368. Zbl0418.10018
  7. [7] A. Nijenhuis, A minimal-path algorithm for the 'money changing problem', Amer. Math. Monthly 86 (1979), 832-834. 
  8. [8] A. Nijenhuis and H. S. Wilf, Representations of integers by linear forms in nonnegative integers, J. Number Theory 4 (1972), 98-106. Zbl0226.10057
  9. [9] G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis I, Springer, 1925 [revised and enlarged: Problems and Theorems in Analysis I , Springer, 1978, pp. 174 and 180 [Problems I 9, I 26-27]. 
  10. [10] Ö. J. Rödseth, Two remarks on linear forms in non-negative integers, Math. Scand. 51 (1982), 193-198. Zbl0503.10035
  11. [11] E. S. Selmer, On the linear diophantine problem of Frobenius, J. Reine Angew. Math. 293/294 (1977), 1-17. Zbl0349.10009
  12. [12] E. S. Selmer, The local postage stamp problem, Part 1: General theory, Ch. II; Part 3: Supplementary volume, Supplement to Ch. II; preprints, University of Bergen, 42 (1986) and 57 (1990), resp. 
  13. [13] Z. Skupień, Exponential constructions of some nonhamiltonian minima, in: Proc. 4th CS Sympos. on Combinat., Graphs and Complexity (held in Prachatice 1990), J. Nešetřil and M. Fiedler (eds.), Ann. Discrete Math. 51, Elsevier, 1992, 321-328. Zbl0763.05068
  14. [14] J. J. Sylvester, [Problem] 7382 (and Solution by W. J. Curran Sharp), The Educational Times 37 (1884), 26; reprinted in (a): Mathematical Questions, with their Solutions, from the 'Educ. Times', with Many Papers (...) 41 (1884), 21. 
  15. [15] H. S. Wilf, A circle-of-lights algorithm for the 'money-changing problem', Amer. Math. Monthly 85 (1978), 562-565. Zbl0387.10009

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