References
N. Alon andM. Dubiner, Zero-sum sets of prescribed size.Combinatorics, Paul Erdös is Eighty, Vol. 1. J. Bolyai Math. Soc, (1993), 33–50.
D. D. Anderson,Factorization in integral domains. Marcel Dekker, 1997.
J. D. Bovey, P. Erdös, andI. Niven, Conditions for zero sum modulon. Canad. Math. Bull 18 (1975), 27–29.
L. Carlitz, A characterization of algebraic number fields with class number two.Proc. AMS 11 (1960), 391–392.
S. Chapman andA. Geroldinger, Krull domains and monoids, their sets of lengths and associated combinatorial problems.Factorization in integral domains. Lecture Notes in Pure Appl. Math. 189. Marcel Dekker (1997), 73–112.
P. Erdös andH. Heilbronn, On the addition of residue classes modulop. Acta Arith. 9 (1964), 149–159.
A. Geroldinger, On non-unique factorizations into irreducible elements II.Colloquia Mathematica Societatis Janos Bolyai 51. North Holland (1987), 723–757.
—, Über nicht-eindeutige Zerlegungen in irreduzible Elemente.Math. Z. 197 (1988), 505–529.
—, Systeme von Längenmengen.Abh. Math. Sem. Univ. Hamburg 60 (1990), 115–130.
—, The cross number of finite abelian groups.J. Number Theory 48 (1994), 219–223.
—, A structure theorem for sets of lengths.Colloq. Math. 78 (1998), 225–259.
W. Gao andA. Geroldinger, Half-factorial domains and half-factorial subsets in abelian groups.Houston J. Math. 24 (1998), 593–611.
—, On long minimal zero sequences in finite abelian groups.Periodica Math. Hungarica 38 (1999), 179–211.
—, On the structure of zerofree sequences.Combinatorica 18 (1998), 519–527.
A. Geroldinger andR. Schneider, The cross number of finite abelian groups II.European J. Combinatorics 15 (1994), 399–405.
—, The cross number of finite abelian groups III.Discrete Math. 150 (1996), 123–130.
W. Gao andY.X. Yang, Note on a combinatorial constant.J. Math. Res. and Expo. 17 (1997), 139–140.
H. Harborth, Ein Extremalproblem für Gitterpunkte.J. Reine Angew. Math. 262 (1973), 356–360.
F. Halter-Koch, Über Längen nicht-eindeutiger Faktorisierungen und Systeme linearer diopantischer Ungleichungen.Abh. Math. Sem. Univ. Hamburg 63 (1993), 265–276.
Y.O. Hamidoune andG. Zémor, On zero-free subset sums.Acta Arith. 78 (1996), 143–152.
F. Kainrath, Factorization in Krull monoids with infinite class group.Colloq. Math. 80 (1999), 23–30.
A. Kemnitz, On a lattice point problem.Ars Combinatoria 16 (1983), 151–160.
W. Narkiewicz,Elementary and Analytic theory of algebraic numbers. Springer, 1990.
J.E. Olson, Sums of sets of group elements.Acta Arith. 28 (1975), 147–156.
J. Sliwa, Remarks on factorizations in algebraic number fields.Coll. Math. 46 (1982), 123–130.
P. van Emde Boas, A combinatorial problem on finite abelian groups II.Reports ZW-1969-007. Math. Centre, Amsterdam, 1969.
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Gao, W., Geroldinger, A. Systems of sets of lengths II. Abh.Math.Semin.Univ.Hambg. 70, 31–49 (2000). https://doi.org/10.1007/BF02940900
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DOI: https://doi.org/10.1007/BF02940900