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On Intersecting Chains in Boolean Algebras

Published online by Cambridge University Press:  12 September 2008

Peter L. Erdős ,
Ákos Seress  and
László A. Székely
Peter L. Erdős
Affiliation:
Centrum voor Wiskunde en Informatica, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands
Ákos Seress
Affiliation:
The Ohio State University, Columbus, OH 43210
László A. Székely
Affiliation:
University of New Mexico, Albuquerque, NM 87131
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Abstract

Analogues of the Erdős-Ko-Rado theorem are proved for the Boolean algebra of all subsets of {1,…n} and in this algebra truncated by the removal of the empty set and the whole set.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 1 , March 1994 , pp. 57 - 62
Copyright
Copyright © Cambridge University Press 1994

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References

[1]Ahlswede, R. and Cai, N. (1993) Incomparability and intersection properties of Boolean interval lattices and chain posets, preprint.Google Scholar
[2]Deza, M. and Frankl, P. (1983) Erdős-Ko-Rado theorem – 22 years later, SIAM J. Alg. Disc. Methods 4, 419–431.CrossRefGoogle Scholar
[3]Erdős, P. L., Faigle, U. and Kern, W. (1992) A group-theoretic setting for some intersecting Sperner families, Combinatorics, Probability and Computing 1, 323–334.Google Scholar
[4]Erdős, P. L., Seress, Á. and Székely, L. A. (1993) On intersecting k-chains in Boolean algebras, Preprint, April 1993.Google Scholar
[5]Erdős, P., Ko, C. and Rado, R. (1961) Intersection theorems for systems of finite sets, Quart. J. Math. Oxford Ser. 2 12, 313–318.CrossRefGoogle Scholar
[6]Frankl, P. (1987) The shifting technique in extremal set theory, In: Whitehead, C. (ed.) Surveys in Combinatorics 1987, Cambridge University Press, 81–110.Google Scholar
[7]Frankl, P. and Füredi, Z. (1980) The Erdős-Ko-Rado theorem for integer sequences, SIAM J. Alg. Disc. Methods 1, 376–381.Google Scholar
[8]Füredi, Z. (1991) Turán type problems, In: Keedwell, A. D. (ed.) Surveys in Combinatorics 1991, Cambridge University Press 253–300.Google Scholar
[9]Lovász, L. (1977) Combinatorial Problems and Exercises, Akadémiai Kiadó, Budapest and North-Holland, Amsterdam.Google Scholar
[10]Simonovits, M. and Sós, V. T., Intersection theorems for graphs. Problèmes Combinatoires et Theorie des Graphes, Coll. Internationaux C.N.R.S. 260 389–391.Google Scholar
[11]Simonovits, M. and Sós, V. T. (1978) Intersection theorems for graphs II. Combinatorics, Coil. Math. Soc. J. Bolyai 18 1017–1030.Google Scholar