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Combinatorics by Peter J. Cameron

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7.  Extremal set theory

Commonest family name. The Chinese name Zhang is borne, according to estimates, by between 9.7 and 12.1 per cent of the Chinese population, so indicating even on the lower estimate that there are at least some 104 million Zhangs.

Peter Matthews (ed.), The Guinness Book of Records (1993).

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TOPICS: Intersecting families; Sperner families; de Bruijn-Erdös Theorem; [regular families]

TECHNIQUES: LYM method

ALGORITHMS:

CROSS-REFERENCES: Hall’s Theorem (Chapter 6); Steiner triple systems (Chapter 8), projective planes (Chapter 9)

Extremal set theory considers families of subsets of a set satisfying some restriction (perhaps in ...

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