ArticleOriginal scientific text
Title
A generalization of Sylvester's and Frobenius' problems on numerical semigroups
Authors 1, 2
Affiliations
- Institute of Mathematics AGH, Academy of Mining and Metallurgy, Mickiewicza 30, 30-059 Kraków, Poland
- Institute of Computer Science, Jagiellonian University, Nawojki 11, 30-072 Kraków, Poland
Bibliography
- J. Bond, Calculating the general solution of a linear Diophantine equation, Amer. Math. Monthly 74 (1967), 955-957.
- A. Brauer and J. E. Shockley, On a problem of Frobenius, J. Reine Angew. Math. 211 (1962), 215-220.
- P. Erdős and R. L. Graham, On a linear diophantine problem of Frobenius, Acta Arith. 21 (1972), 399-408.
- R. Fröberg, C. Gottlieb and R. Häggkvist, On numerical semigroups, Semigroup Forum 35 (1987), 63-83.
- S. Kertzner, The linear diophantine equation, Amer. Math. Monthly 88 (1981), 200-203.
- S. Morito and H. M. Salkin, Finding the general solution of a linear diophantine equation, Fibonacci Quart. 17 (1979), 361-368.
- A. Nijenhuis, A minimal-path algorithm for the 'money changing problem', Amer. Math. Monthly 86 (1979), 832-834.
- A. Nijenhuis and H. S. Wilf, Representations of integers by linear forms in nonnegative integers, J. Number Theory 4 (1972), 98-106.
- 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].
- Ö. J. Rödseth, Two remarks on linear forms in non-negative integers, Math. Scand. 51 (1982), 193-198.
- E. S. Selmer, On the linear diophantine problem of Frobenius, J. Reine Angew. Math. 293/294 (1977), 1-17.
- 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.
- 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.
- 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.
- H. S. Wilf, A circle-of-lights algorithm for the 'money-changing problem', Amer. Math. Monthly 85 (1978), 562-565.