| 1. | And the corresponding operation of symmetric functions is the usual product.
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| 2. | The study of symmetric functions is based on that of symmetric polynomials.
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| 3. | Expressed as identities of in the ring of symmetric functions, they read
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| 4. | The second definition of the ring of symmetric functions implies the following fundamental principle:
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| 5. | In other words, it is a symmetric function of the pair of triangles.
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| 6. | This phenomenon can be understood in the setting of the ring of symmetric functions.
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| 7. | A ring of this kind plays a role in constructing the ring of symmetric functions.
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| 8. | A symmetric function is a function that is unchanged when two variables and are interchanged:
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| 9. | His 1979 book " Symmetric Functions and Hall Polynomials " has become a classic.
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| 10. | They were introduced by the mathematician Carl Kostka in his study of symmetric functions ( ).
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