Statements (14)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:inequality
|
| gptkbp:appliesTo |
symmetric sums
|
| gptkbp:field |
gptkb:algebra
symmetric polynomials |
| gptkbp:generalizes |
gptkb:AM-GM_inequality
|
| https://www.w3.org/2000/01/rdf-schema#label |
Muirhead's inequality
|
| gptkbp:namedAfter |
gptkb:Robert_Franklin_Muirhead
|
| gptkbp:publicationYear |
1902
|
| gptkbp:publishedIn |
gptkb:Proceedings_of_the_Edinburgh_Mathematical_Society
|
| gptkbp:requires |
majorization
|
| gptkbp:sentence |
If (a_1, ..., a_n) majorizes (b_1, ..., b_n), then the sum over all permutations of the product of x_i^{a_i} is at least as large as the sum over all permutations of the product of x_i^{b_i}, for non-negative real numbers x_i.
|
| gptkbp:usedIn |
inequality proofs
|
| gptkbp:bfsParent |
gptkb:Schur's_inequality
|
| gptkbp:bfsLayer |
7
|