By Ian Anderson

The combinatorial learn of finite set structures is a full of life sector of analysis unified by way of the sluggish discovery of structural insights and commonly appropriate evidence innovations. This booklet is the 1st coherent and up to date account of the elemental equipment and result of this research. a lot of the cloth within the booklet issues subsets of a collection, yet chapters additionally disguise extra basic partly ordered units. for instance, the Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is mentioned, as is the Greene-Kleitman outcome bearing on k-saturated chain walls of normal in part ordered units. Connections with Dilworth's theorem, the wedding challenge, and likelihood are awarded. every one bankruptcy ends with a set of workouts for which define recommendations are supplied, and there's an intensive bibliography. The paintings is necessary for postgraduate scholars and researchers in discrete arithmetic and comparable matters

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Wait, in order to continue, we need a second piece of notation! Ordered ntuples (a, b, . . , n) are members of the set denoted A × B × · · · × N, called the Cartesian product of the sets A, B, . . , N. The product principle. The number of elements in the Cartesian product of a finite number of finite sets A × B × · · ·× N is the product of their sizes |A| · |B| · · · · · |N|. 2, where we might consider |A| = 6 and |B| = 3. The same Cartesian product can be grouped as |B| copies of A, or as |A| copies of B.

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