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- Monk's_formula abstract "In mathematics, Monk's formula, found by Monk (1959), is an analogue of Pieri's formula that describes the product of a linear Schubert polynomial by a Schubert polynomial. Equivalently, it describes the product of a special Schubert cycle by a Schubert cycle in the cohomology of a flag manifold.Write tij for the transposition (i j), and si = ti,i+1. Then 𝔖sr = x1 + ⋯ + xr, and Monk's formula states that for a permutation w,where is the length of w. The pairs (i, j) appearing in the sum are exactly those such that i ≤ r < j, wi < wj, and there is no i < k < j with wi < wk < wj; each wtij is a cover of w in Bruhat order.".
- Monk's_formula wikiPageID "22444842".
- Monk's_formula wikiPageRevisionID "489897433".
- Monk's_formula hasPhotoCollection Monk's_formula.
- Monk's_formula subject Category:Symmetric_functions.
- Monk's_formula type Abstraction100002137.
- Monk's_formula type Function113783816.
- Monk's_formula type MathematicalRelation113783581.
- Monk's_formula type Relation100031921.
- Monk's_formula type SymmetricFunctions.
- Monk's_formula comment "In mathematics, Monk's formula, found by Monk (1959), is an analogue of Pieri's formula that describes the product of a linear Schubert polynomial by a Schubert polynomial. Equivalently, it describes the product of a special Schubert cycle by a Schubert cycle in the cohomology of a flag manifold.Write tij for the transposition (i j), and si = ti,i+1. Then 𝔖sr = x1 + ⋯ + xr, and Monk's formula states that for a permutation w,where is the length of w.".
- Monk's_formula label "Monk's formula".
- Monk's_formula sameAs m.05zhyb7.
- Monk's_formula sameAs Q17043011.
- Monk's_formula sameAs Q17043011.
- Monk's_formula sameAs Monk's_formula.
- Monk's_formula wasDerivedFrom Monk's_formula?oldid=489897433.
- Monk's_formula isPrimaryTopicOf Monk's_formula.