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The Spectrum of a Finite Lattice: Breadth and Length Techniques

Published online by Cambridge University Press:  20 November 2018

Richard Nowakowski  and
Ivan Rival
Richard Nowakowski
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, CanadaT2N IN4
Ivan Rival
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, CanadaT2N IN4
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Efforts to determine the orders of the sublattices of an arbitrary finite lattice date back at least to the early 1930's, and notably, in the work of Fritz Klein-Barmen [3], [4]. Nevertheless, very little that is new has appeared in the literature since that time.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 3 , 01 September 1977 , pp. 319 - 329
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Dilworth, R. P., A decomposition theorem for partially ordered sets, Ann. Math. 51 (1950), 161-166.Google Scholar
2. Kelly, D. and Rival, I.. Crowns, fences and dismantlable lattices, Canad. J. Math. 26 (1974). 1257-1271.Google Scholar
3. Klein-Barmen, Fr., Grundzüge der Théorie der Verbànde, Math. Ann. 111 (1935), 596-621.Google Scholar
4. Klein-Barmen, Fr., Birkhoffsche und harmonische Verbànde, Math. Zeit. 42 (1937). 58-81.Google Scholar
5. Rival, I., Finite modular lattices with sublattices of all orders, Notices Amer. Math. Soc. (1973), *73T-A38.Google Scholar
6. Rival, I., Lattices with doubly irreducible elements, Canad. Math. Bull. 17 (1974), 91-95.Google Scholar