A generalization of Sylvester's and Frobenius' problems on numerical semigroups
Zdzisław Skupień
Acta Arithmetica, Tome 64 (1993), p. 353-366 / Harvested from The Polish Digital Mathematics Library
Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:206585
@article{bwmeta1.element.bwnjournal-article-aav65i4p353bwm,
     author = {Zdzis\l aw Skupie\'n},
     title = {A generalization of Sylvester's and Frobenius' problems on numerical semigroups},
     journal = {Acta Arithmetica},
     volume = {64},
     year = {1993},
     pages = {353-366},
     zbl = {0789.11017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav65i4p353bwm}
}
Zdzisław Skupień. A generalization of Sylvester's and Frobenius' problems on numerical semigroups. Acta Arithmetica, Tome 64 (1993) pp. 353-366. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav65i4p353bwm/

[000] [1] J. Bond, Calculating the general solution of a linear Diophantine equation, Amer. Math. Monthly 74 (1967), 955-957. | Zbl 0159.05902

[001] [2] A. Brauer and J. E. Shockley, On a problem of Frobenius, J. Reine Angew. Math. 211 (1962), 215-220. | Zbl 0108.04604

[002] [3] P. Erdős and R. L. Graham, On a linear diophantine problem of Frobenius, Acta Arith. 21 (1972), 399-408. | Zbl 0246.10010

[003] [4] R. Fröberg, C. Gottlieb and R. Häggkvist, On numerical semigroups, Semigroup Forum 35 (1987), 63-83. | Zbl 0614.10046

[004] [5] S. Kertzner, The linear diophantine equation, Amer. Math. Monthly 88 (1981), 200-203. | Zbl 0458.10014

[005] [6] S. Morito and H. M. Salkin, Finding the general solution of a linear diophantine equation, Fibonacci Quart. 17 (1979), 361-368. | Zbl 0418.10018

[006] [7] A. Nijenhuis, A minimal-path algorithm for the 'money changing problem', Amer. Math. Monthly 86 (1979), 832-834.

[007] [8] A. Nijenhuis and H. S. Wilf, Representations of integers by linear forms in nonnegative integers, J. Number Theory 4 (1972), 98-106. | Zbl 0226.10057

[008] [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].

[009] [10] Ö. J. Rödseth, Two remarks on linear forms in non-negative integers, Math. Scand. 51 (1982), 193-198. | Zbl 0503.10035

[010] [11] E. S. Selmer, On the linear diophantine problem of Frobenius, J. Reine Angew. Math. 293/294 (1977), 1-17. | Zbl 0349.10009

[011] [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.

[012] [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. | Zbl 0763.05068

[013] [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.

[014] [15] H. S. Wilf, A circle-of-lights algorithm for the 'money-changing problem', Amer. Math. Monthly 85 (1978), 562-565. | Zbl 0387.10009