Partition Regularity
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the notion of partition regularity in combinatorics is one approach to explaining when a set system is quite large. The collection of all infinite subsets of an infinite set X is a prototypical example. In this case partition regularity asserts that every finite partition of an infinite set has an infinite cell (i.e. the infinite pigeonhole principle.) Call a subset of natural numbers i.p.-rich if it contains arbitrarily large finite sets together with...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the notion of partition regularity in combinatorics is one approach to explaining when a set system is quite large. The collection of all infinite subsets of an infinite set X is a prototypical example. In this case partition regularity asserts that every finite partition of an infinite set has an infinite cell (i.e. the infinite pigeonhole principle.) Call a subset of natural numbers i.p.-rich if it contains arbitrarily large finite sets together with all their finite sums. Then the collection of i.p.-rich subsets is partition regular (Folkman Rado Sanders, 1968).
