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Threshold Progressions in a Variety of Covering and Packing Contexts

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 نشر من قبل Anant Godbole
 تاريخ النشر 2018
  مجال البحث
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Using standard methods (due to Janson, Stein-Chen, and Talagrand) from probabilistic combinatorics, we explore the following general theme: As one progresses from each member of a family of objects ${cal A}$ being covered by at most one object in a random collection ${cal C}$, to being covered at most $lambda$ times, to being covered at least once, to being covered at least $lambda$ times, a hierarchy of thresholds emerge. We will then see how such results vary according to the context, and level of dependence introduced. Examples will be from extremal set theory, combinatorics, and additive number theory.



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