Tableaux and chains in a new partial order of \(S_ n\) (Q1119668)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Tableaux and chains in a new partial order of \(S_ n\) |
scientific article; zbMATH DE number 4097441
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Tableaux and chains in a new partial order of \(S_ n\) |
scientific article; zbMATH DE number 4097441 |
Statements
Tableaux and chains in a new partial order of \(S_ n\) (English)
0 references
1989
0 references
The set of all permutations of the set ṉ\(=\{1,...,n\}\) may be partially ordered by the rule \(\sigma\leq \tau \Leftrightarrow (I(\sigma)\subseteq I(\tau)\) and if (j,i)\(\in I(\tau)-I(\sigma)\) then for all \(k\in \underline n\), \(\sigma^{-1}(k)<\sigma^{-1}(j)\) implies that \(k<j)\), where \(I(\rho)=\{(j,i)|\) \(i<j\), \(\rho^{-1}(j)<\rho^{- 1}(i)\}\). Some facts about this partial order are proved.
0 references
symmetric group
0 references
weak ordering
0 references
maximal chains
0 references
shifted tableaux
0 references
convex geometries
0 references
