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Results tagged with symmetric-functions
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user 122662
Symmetric functions are symmetric polynomials, in finitely many, or countably infinitely many variables. They arise in the representation theory of symmetric groups and in the polynomial representation theory of general linear groups. Bases of the ring of symmetric functions are indexed by integer partitions. Schur functions, elementary symmetric functions, complete symmetric functions, and power sum symmetric functions are the most commonly used bases.
8
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1
answer
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A Muirhead Like Inequality
I am looking for a proof of the inequality as follow:
Let $n$ be an integer number $n \ge 2$ and $x_1, \cdots, x_n$ and $y_1,\cdots, y_n$ are nonegative real numbers such that $(x_1,\cdots, x_n)$ …
- 1,776
4
votes
2
answers
428
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Combination power elementary symmetric polynomial inequality
Combine my first previous question and second previous question with the Muirhead inequality. I have posed conjectures of two inequalities as follows:
Inequality 1: Let $n>2$ and $1 \le m \le n$ …
- 1,776
2
votes
0
answers
359
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An inequality related to Power sum and elementary symmetric polynomial and majorizes
Power sum and elementary symmetric polynomial
Let $x_1,. . . , x_n$ be variables, denote for $k \ge 1$ by $p_k(x_1,\dots,x_n)$ the $k-th$ power sum:
$$ p_k(x_1,\dots,x_n)=\sum\nolimits_{i=1}^nx_i^ …
- 1,776
0
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Combination power elementary symmetric polynomial inequality
This is not an answer, this is a message to @Gjergji Zaimi. Thank You very much. (And thank to dear Wolfgang very much). Your answer is true with the version above. But if You see my comment to You a …
- 1,776
0
votes
2
answers
368
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A symmetric polynomial inequality
I improve my previous question. Because this conjecture is exactly natural development of A Muirhead Like Inequality and Muirhead's Inequality so I think the conjecture is true. But I can not prove it …
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