Hostname: page-component-7c8c6479df-94d59 Total loading time: 0 Render date: 2024-03-29T11:19:35.035Z Has data issue: false hasContentIssue false

On Intersecting Chains in Boolean Algebras

Published online by Cambridge University Press:  12 September 2008

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

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.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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, 419431.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, 323334.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, 313318.CrossRefGoogle Scholar
[6]Frankl, P. (1987) The shifting technique in extremal set theory, In: Whitehead, C. (ed.) Surveys in Combinatorics 1987, Cambridge University Press, 81110.Google Scholar
[7]Frankl, P. and Füredi, Z. (1980) The Erdős-Ko-Rado theorem for integer sequences, SIAM J. Alg. Disc. Methods 1, 376381.Google Scholar
[8]Füredi, Z. (1991) Turán type problems, In: Keedwell, A. D. (ed.) Surveys in Combinatorics 1991, Cambridge University Press 253300.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 389391.Google Scholar
[11]Simonovits, M. and Sós, V. T. (1978) Intersection theorems for graphs II. Combinatorics, Coil. Math. Soc. J. Bolyai 18 10171030.Google Scholar