About: Partition regularity

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In combinatorics, a branch of mathematics, partition regularity is one notion of largeness for a collection of sets. Given a set , a collection of subsets is called partition regular if every set A in the collection has the property that, no matter how A is partitioned into finitely many subsets, at least one of the subsets will also belong to the collection. That is,for any , and any finite partition , there exists an i ≤ n, such that belongs to . Ramsey theory is sometimes characterized as the study of which collections are partition regular.

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  • التجزئة المنتظمة في الرياضيات هي تقسيم فترة أعداد حقيقية إلى أطوال متساوية، يسمى العنصر الأول فيها ويسمى العنصر الأخير فيها . عدد الفترات الجزئية لها يساوي عدد عناصرها -1، والعكس أيضا فان عدد عناصرها بساوي عدد الفترات الجزئية فيها +1. (ar)
  • In combinatorics, a branch of mathematics, partition regularity is one notion of largeness for a collection of sets. Given a set , a collection of subsets is called partition regular if every set A in the collection has the property that, no matter how A is partitioned into finitely many subsets, at least one of the subsets will also belong to the collection. That is,for any , and any finite partition , there exists an i ≤ n, such that belongs to . Ramsey theory is sometimes characterized as the study of which collections are partition regular. (en)
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  • التجزئة المنتظمة في الرياضيات هي تقسيم فترة أعداد حقيقية إلى أطوال متساوية، يسمى العنصر الأول فيها ويسمى العنصر الأخير فيها . عدد الفترات الجزئية لها يساوي عدد عناصرها -1، والعكس أيضا فان عدد عناصرها بساوي عدد الفترات الجزئية فيها +1. (ar)
  • In combinatorics, a branch of mathematics, partition regularity is one notion of largeness for a collection of sets. Given a set , a collection of subsets is called partition regular if every set A in the collection has the property that, no matter how A is partitioned into finitely many subsets, at least one of the subsets will also belong to the collection. That is,for any , and any finite partition , there exists an i ≤ n, such that belongs to . Ramsey theory is sometimes characterized as the study of which collections are partition regular. (en)
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  • تجزئة منتظمة (ar)
  • Partition regularity (en)
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