Skip to main content
Log in

Shadows and shifting

  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

It is shown how the shifting technique can be used to provide lower bounds on the shadows of families with specific intersection and union properties.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Erdös, P., Ko, C., Rado, R.: Intersection theorems for systems of finite sets. Q. J. Math. Oxford12, 313–320 (1961)

    Google Scholar 

  2. Frankl, P.: A new short proof of the Kruskal-Katona theorem. Discrete Math.48, 327–329 (1984)

    Google Scholar 

  3. Frankl, P.: Generalizations of theorems of Katona and Milner. Acta Math. Acad. Sci. Hung.27, 359–363 (1976)

    Google Scholar 

  4. Frankl, P.: New proofs for old theorems in extremal set theory. Proc. Indian Comb. Conf., Calcutta1982 ISI 127–132 (1985)

    Google Scholar 

  5. Frankl, P.: The shifting technique in extremal set theory. Proc. 11th British Comb. Conf., (C. Whitehead, ed.) LMS Lecture Notes pp. 81–110

  6. Frankl, P., Füredi, Z.: Hypergraphs without two edges intersecting in a given number of vertices. J. Comb. Theory (A)36, 230–236 (1984)

    Google Scholar 

  7. Katona, G.O.H.: A theorem of finite sets, in Theory of Graphs. Proc. Comb. Conf. held at Tihany, Hungary 187–207 (1966)

  8. Katona, G.O.H.: Intersection theorems for systems of finite sets. Acta Math. Acad. Sci. Hung.15, 329–337 (1964)

    Google Scholar 

  9. Katona, G.O.H.: Problem 11, Mathematikus Kurir, 1983

  10. Kruskal, J.B.: The number of simplicies in a complex, in “Mathematical Optimization Techniques”, pp. 251–278. Berkeley: Univ. California Press, 1963

    Google Scholar 

  11. Quinn, F.: Ph.D. Thesis, MIT, 1987

  12. Sperner, E.: Ein Satz über Untermengen einer endlichen Menge. Math. Z.,27, 544–548 (1928)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Frankl, P. Shadows and shifting. Graphs and Combinatorics 7, 23–29 (1991). https://doi.org/10.1007/BF01789460

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01789460

Keywords

Navigation