Sequences of ordered sets and Catalan numbers (Q1970926)
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scientific article; zbMATH DE number 1423846
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sequences of ordered sets and Catalan numbers |
scientific article; zbMATH DE number 1423846 |
Statements
Sequences of ordered sets and Catalan numbers (English)
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7 June 2000
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A nonincreasing sequence \((d_1,\ldots,d_n)\) of non-negative integers is a down set sequence if there is a (partially) ordered set \(\{x_1,\ldots,x_n\}\) s.t. the cardinality of the downset of \(x_i\) is \(d_i.\) It is shown that the number of \(n\)-element down set sequences is just the \(n\)th Catalan number.
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Catalan numbers
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down set sequences
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