Width of a partially ordered set
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This category corresponds roughly to MSC {{{id}}} {{{title}}}; see {{{id}}} at MathSciNet and {{{id}}} at zbMATH.
Dilworth number, Sperner number
The greatest possible size of an anti-chain (set of mutually incomparable elements) in a partially ordered set. A partially ordered set of width 1 is a chain (totally ordered set).
Dilworth's theorem [1] states that in a finite partially ordered set the width is equal to the minimal number of chains that cover the set.
See also Sperner property.
References
| [1] | R.P. Dilworth, "A decomposition theorem for partially ordered sets" Ann. of Math. , 51 (1950) pp. 161–166 Template:ZBL |
| [2] | George Grätzer, General Lattice Theory, Springer (2003) ISBN 3764369965 Template:ZBL |
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