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On Möbius Functions and a Problem in Combinatorial Number Theory

Published online by Cambridge University Press:  20 November 2018

Bernt Lindström*
Affiliation:
University of Stockholm, Stockholm, Sweden
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After the publication of the important paper by Rota [9] on Möbius functions a large number of papers have appeared in which the ideas are applied or generalized in various directions, the papers by Crapo [3], Smith [10] and Tainiter [11] are some of them. The theory of Möbius functions is now recognized as a valuable tool in combinatorial and arithmetical research.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. 1, Amer. Math. Soc. 1961.Google Scholar
2. Conway, J. H. and Guy, R. K., Notices Amer. Math. Soc. 15, 1969, p. 345.Google Scholar
3. Crapo, H. H., Möbius inversion in lattices, Arch. Math. XIX, (1968), 595-607.Google Scholar
4. Erdös, P., Quelques problèmes de la théorie des nombres, Mon. L'Enseign. Math. 6, Genève, Problème 30, Soc. Math. Suisse, 1963, p. 101.Google Scholar
5. Lindström, B., On a combinatorial problem in number theory, Canad. Math. Bull. 8 (1965), 477-490.Google Scholar
6. Lindström, B., Determinants on semilattices, Proc. Amer. Math. Soc. 20 (1969), 207-208.Google Scholar
7. Lindström, B.,Qn tne realization of convex polytopes, Euler's formula and Möbius functions, Aequationes Math., (to appear).Google Scholar
8. Lindström, B. and Zetterström, H.-O., A combinatorial problem in the k-adic number system, Proc. Amer. Math. Soc. 18 (1967), 166-170.Google Scholar
9. Rota, G.-C., On the foundations of combinatorial theory, I Theory of Möbius functions, Z. Wahrsch. 2 (1964), 340-368.Google Scholar
10. Smith, D., Incidence functions as generalized arithmetic functions, I, II, III, Duke Math. J. 34, 1967, pp. 617–634, 36, 1969, pp. 15-30, 353–368.Google Scholar
11. Tainiter, M., Generating functions on idempotent semigroups with application to combinatorial analysis, J. Combinatorial Theory 5 (1968), 273-288.Google Scholar