A Homological Approach to Two Problems on Finite Sets
Rita Csákány
and Jeff Kahn
DOI: 10.1023/A:1018630111976
Abstract
We propose a homological approach to two conjectures descended from the Erdös-Ko-Rado Theorem, one due to Chvátal and the other to Frankl and Füredi. We apply the method to reprove, and in one case improve, results of these authors related to their conjectures.
Pages: 141–149
Keywords: extremal problem; finite set; Erdös-ko-rado theorem
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References
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2. R. Csákány, Ph.D. Thesis, Rutgers University, 1997.
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5. P.J. Hilton and S. Wylie, Homology Theory, Cambridge University Press, Cambridge, 1965.
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2. R. Csákány, Ph.D. Thesis, Rutgers University, 1997.
3. P. Erd\Acute\Acute os, C. Ko, and R. Rado, “Intersection theorems for systems of finite sets,” Quart. J. Math. Oxford (2) 12 (1961), 313-320.
4. P. Frankl and Z. F\ddot uredi, “Exact solution of some Turán-type problems,” J. Comb. Theory Ser. A 45 (1987), 226-262.
5. P.J. Hilton and S. Wylie, Homology Theory, Cambridge University Press, Cambridge, 1965.
6. D.J.A. Welsh, Matroid Theory, Academic Press, London, 1976.