Chains, subwords, and fillings: strong equivalence of three definitions of the Bruhat order (Q819190)
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scientific article; zbMATH DE number 5014325
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Chains, subwords, and fillings: strong equivalence of three definitions of the Bruhat order |
scientific article; zbMATH DE number 5014325 |
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Chains, subwords, and fillings: strong equivalence of three definitions of the Bruhat order (English)
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22 March 2006
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Summary: Let \(S_n\) be the group of permutations of \([n]=\{1,\dots,n\}\). The Bruhat order on \(S_n\) is a partial order relation, for which there are several equivalent definitions. Three well-known conditions are based on ascending chains, subwords, and comparison of matrices, respectively. We express the last using fillings of tableaux, and prove that the three equivalent conditions are satisfied in the same number of ways.
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