An interpretation for Garsia and Remmel's \(q\)-hit numbers (Q1380346)
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scientific article; zbMATH DE number 1123556
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An interpretation for Garsia and Remmel's \(q\)-hit numbers |
scientific article; zbMATH DE number 1123556 |
Statements
An interpretation for Garsia and Remmel's \(q\)-hit numbers (English)
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4 March 1998
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Garsia and Remmel's \(q\)-analogue of the rook numbers and hit numbers associated with a Ferrers board is studied. A new recurrence for these \(q\)-hit numbers is found. Also, a statistic on permutations that constitutes a direct combinatorial interpretation of the \(q\)-hit numbers is defined. The statistic is used to prove a reciprocity theorem.
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\(q\)-analogue
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rook numbers
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hit numbers
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Ferrers board
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statistic
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reciprocity theorem
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