| 11. | Extremal combinatorics studies extremal questions on set systems.
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| 12. | Extremal combinatorics studies extremal questions on set systems.
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| 13. | Ramsey theory is another part of extremal combinatorics.
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| 14. | Until recently, prospects for useful extremal principles in this area have seemed clouded.
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| 15. | Other writers have also felt that prospects for general global extremal principles are clouded.
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| 16. | The condition allows one to prove that a corner exists along a given extremal.
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| 17. | Extremal states are usually called pure states.
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| 18. | Extremal black holes have vanishing surface gravity.
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| 19. | Several foundational results in extremal graph theory are questions of the above-mentioned form.
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| 20. | The two areas that interest him most are extremal graph theory and random graph theory.
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